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1. Click to play the video Modellus 2 5 PASCO Videos pp f asco avi asco avi asco avi i E 1994 i i E atlas rocket j all gi Prev Next gt Faculdade de Ci ncias e Tecnologia y T Iniversidade Nnva de iehna Modellus Manual version 2 5 2002 blank page Modellus Manual version 2 5 2002 Scientific computation has become so much a part of everyday experience of scientific and engineering practice that it can be considered a third fundamental methodology of science parallel to the more established paradigms of experimental and theoretical science National Research Council National Academy of Sciences USA Introduction Building and exploring mathematical models is a fundamental task in science Modellus offers students and teachers a minds on multilevel learning experience in which they create simulate and analyze models interactively on the computer either from experimental data and images or from pure theoretical thinking Modellus is software for interactive modelling with mathematics Teachers and students can use Modellus to build mathematical models and explore them as animations graphs and tables Instead of just looking at algebraic differential and iterative equations Modellus users can experiment visually and interactively with models and animations to better understand the underlying mathematics and the multiple representations of a model2. The results momentum after momentun momentum after before My conclusion is that Descartes was tight 57 Modellus Manual version 2 5 2002 INTERMEDIATE 22 While the simulation is running you can affect the results by interacting with the variables that control objects in the Animation window For example you can create an Animation 1 interactive level indicator for a variable and use the level indicator during simulation to alter the variable QHOOB o XI EPA Min 10 00 Max 10 00 With a single mouse click you can change the value assigned to a Digital Meter During an animated simulation simply grab the Digital Meter object and then click the left mouse button Modellus pauses the simulation and opens the Value dialog box Type the new value in the text box Click OK The simulation resumes play using QGHOO O 0B uso the new value you entered C Cancel Copy window contents to the clipboard 58 Modellus Manual version 2 5 2002 INTERMEDIATE lc ols in the Animation 23 Select a tool and then click with the left button to start measuring Keep clicking with the left button to proceed with the measurement End the measurement by clicking with the right button After creating a measuring tool you can adjust the points of the tool with the left button HORIZONTAL VERTICAL Scales To edit or delete a measuring tool use
3. In the Control window you can e Run gt or pause the model e Stop O the model e Rewind cl the model without losing calculated values Control DOC e Jump to the last value of the model Replay the model Independent variable t Step IH e Read T 4 30 the current value of the independent variable and the limits of its domains i MiO Molo e Drag N Em e current Nw value of the independent variable and check visually amp Degrees OBadians the progress of the variable E E Output e Go backward 4 or forward a single step vaalia DIRIGERE 2 e Access the Options dialog box PIET SU Model type Iterative I Auto Run on Open Cancel Use the Options dialog box to e Set the limits and the step of the independent variable e Choose the angle unit e Format all numbers in tables graphs animations and in the Initial Conditions window e Change the model type from standard with an explicit independent variable to an iterative model without explicit independent variable e Check uncheck to auto run when loading the model 41 Modellus Manual version 2 5 2002 1 imported images references dialog Ox INTERMEDIATE 6 Modellus files have an mdl extension The filename must be a valid Windows filename e g it can t use symbols like V lt gt Modellus files can be launched locally from a web browser or other software with
4. particle moving with constant velocity Font Colour mu HORIZONTAL VERTICAL Origin Scales 1 Pixel 1Pixel h Cancel Delete Helease 32 Modellus Manual version 2 5 2002 20metric object in the ation window E Animation 1 CO on i m n El a iaia AI ATA E VMA Click on the Geometric Object button Click in the Animation window Geometric Object x Type Point No of points Name Object no 52 Points PI I Select Type Circle segment Attributes M Name Polygon E Circle Colour MN F Value O Line Thickness 2 m Change Colour and Pointe M Axis Thickness HORIZONTAL VERTICAL Scales Filled Tracking Click Placement Origin Var Axes Var Axes Track every 10 steps i Cancel Delete Select Center on HORIZONTAL VERTICAL COOFAIMALES 0 2 Center NN NM and Point on x 0 Point NEN Cancel Click OK and run the model 33 Modellus Manual version 2 5 2002 18 Help Menu E Modellus 2 5 Ea x C c fm Help Show Back Forward Home Dep Workshops and Help Modellus Workshops and Help Version 2 5 2002 About Modellus Workshops Exploring Graph 1 The Help file has four radios dat E A Bin a Velocity and Acceleration with Differential Equations Workshops that introduce Analysing a Graph of erimental Data and Creating an
5. If a gt O then sign a 1 If a O then sign a O 69 Modellus Manual version 2 5 2002 Example If t lt 10 then a 0 5 If t gt 10 then a 0 5 If t lt gt 10 then a 0 2 If t 1 then a 0 5 If t gt 1 then a 0 2 If t lt 1 then a 0 2 if t gt 1 and r lt 5 then a 0 2 If t gt 1 or r lt 5 then a 0 2 Description If the variable t is less than 10 then the variable a is 0 5 If there is no other control statement the variable a will always be 0 5 If the variable t is greater than 10 then the variable a is 0 5 If the variable t is different from 10 then the variable a is 0 2 When tis 1 a is 0 5 If the variable t is greater than or egual to 1 then the variable a is 0 2 If the variable t is less than or egual to 1 then the variable a is 0 2 If there is no other control statement the variable a will always be 0 2 If the variable t is greater than 1 and the variable r is less than 5 then the variable a is 0 2 If the variable t is greater than 1 or the variable r is less than 5 then the variable a is 0 2 If the variable switch is egual 1 If switch 0 then ambda wavelength x 1 and b 5 to O then lambda is equal to and b is 5 if switch 1 then ambda wavelength and b 10 If the variable switch is equal If y lt 0 then a stop t If t 5 then a pause t If t 5 then a pause2 10 to 1 then ambda is equal to wav
6. gt Interactive Modelling with Mathematics Mode Modellus Manual version 2 5 2002 blank page Modellus Manual version 2 5 2002 Modellus 5 Aurhors Interac Vitor Duarte Teodoro Jo o Paulo Duque Vieira K Filipe Casta Cl rigo with Matbemati Faculry of Sciences and Technology Nova University Lisbon Portugal FCTUNL version 2 5 2002 FCTUNL and Knowledge evolu Thanks ta George Birbilis versio Afren rag Jc iprpmpnid This User s Manual for Modellus 2 5 was written by Vitor Duarte Teodoro Copyright O FCTUNL 2002 All rights reserved Copyright O Knowledge Revolution 1997 Modellus 1 0 was available from Knowledge Revolution www krev com 66 Bovet Road Suite 200 San Mateo California 94402 USA Modellus 2 5 is available from Faculty of Sciences and Technology www fct unl pt New University of Lisbon www unl pt Portugal For further information see next pages Modellus Manual version 2 5 2002 blank page Modellus Manual version 2 5 2002 Modellus web page and support For updated information see http phoenix sce fct unl pt modellus Modellus web page Microsoft Internet Explorer Ex File Edit View Favorites Tools Help Ossk O HMO d Address http phoenix sce fct unl pt modellus For email support and information send an email to modellus mail fct unl pt Google Bo Search Web R Search Site PageRank O Page
7. D const Attributes Name M Value Change Position C Size from lower left Scales Origin Var Axes bd Var Axes gt Image from file Cancel Delete Size from center 79 Modellus Manual version 2 5 2002 orter properties II Size from Lower Left Variation affects how Modellus scales the image s size in the Animation window In this case the image grows outward from the lower left corner of its bounding box To specify The variable that controls the image s horizontal size The variable that controls the image s vertical size The variable that controls the horizontal position of the origin of the image s axis The variable that controls the vertical position of the origin of the image s axis Do this Select it in the Horizontal list box Select it in the Vertical list box Under Origin select the appropriate variable in the Horizontal list box Under Origin select the appropriate variable in the Vertical list box Image Importer x HORIZONTAL VERTICAL Name Ui Goes Attributes Name M Value scales Origin Var Axes gt Var Axes bd Change amp Position Size from lower left C Size from center Image from file Do meses Cancel Delete 80 Modellus Manual version 2 5 2002 orter properties III Size from Centre Variation also affects how Modellus scales the image s size in the Animation window
8. Release When prompted to edit object greenball click No When prompted to edit object velocity click Yes The Vector properties dialog box appears At the top of the dialog box Modellus shows you the name of the object the vector is attached to In the Vector properties dialog box click the Release button and then click OK Modellus releases the attachment between the objects When you release one object from another first identify the object from which the attachment was initiated For example if you attached a vector to a ball you must release the vector from the ball as described in the preceding steps Note If the Release button is disabled in the object s properties dialog box then the attachment was not initiated from that object 56 INTERMEDIATE 21 Modellus Manual version 2 5 2002 To copy the entire contents of the Animation window as an image and paste it into another application choose Copy Window from the Edit menu or click the Copy button at the top right of the Animation window After pasting in Word Animation 1 CN si a m a E ETSI S Ae mitit H momentum after momentu momentum after before Microsoft Word Document N 01 X w File Edit View Insert Format Tools Table Window Help m laj x celal ans sael e ala as fo QIN Normal Times New Roman fio B u 4 E Pr pra doe e e porn Qr ror por Gar por rd rr n
9. Type a value in the appropriate Scale text box Choose a colour from the Colour pop up menu Choose a thickness from the Thickness pop up menu Toggle the Name attribute checkbox to show or hide the names of variables Toggle the Value attribute checkbox to show or hide the values assigned to variables Toggle the Axis attribute checkbox to show or hide the plotter s axes Toggle the Pencil attribute checkbox to show or hide the pencil Toggle the Projection Lines attribute checkbox to show or hide projection lines Select Points to draw points instead of a line Select Line to draw a HORIZONTAL VERTICAL Attributes line instead i A Name of points v UE M Axis M Pencil Iv Projection Lines C Points Line Colour EN Thickness 1 Cancel Delete Scales 77 Modellus Manual version 2 5 2002 meter properties To specify Do this The variable value you want to display Select the variable in the Variable list box The variables that control the location of the Select the appropriate variables in the Origin list digital meter s origin boxes The scale of the digital meter s vertical or Type a value in the appropriate Scale text box horizontal movement on the screen The scaling factor should match the scaling specified for the variable that controls the origin s location Colour for text alphanumeric Choose a colour from the Colour pop up menu Font for text alphanum
10. t lasti di Euler method STE E Cases M step JOKINEN ES i5LAN _U WI 000000000 0 10000000 000000000 Initial values 0 00500000 0 1 0000000 0 4 0000000 t 0 01000000 0 09950000 0 20000000 hs 7 dt 0 01 497500 0 09850000 0 30000000 jm Dam 0 01990000 0 09700250 040000000 M i D 02475012 0 09504 250 0 50000000 0 02950075 0 092537 49 0 60000000 0 0341 2762 0 08955741 0 70000000 0 03860699 0 0861 7465 0 80000000 0 04291573 0 08231395 0 90000000 0 04703143 1 00000000 65 Modellus Manual version 2 5 2002 blank page 66 Modellus Manual version 2 5 2002 REFERENCE 67 Modellus Manual version 2 5 2002 blank page 68 Function Square root Sine Co sine Tangent Secant Co secant Co tangent Arc sine Arc co sine Arc tangent Natural logarithm Decimal logarithm Hyperbolic sine 2 Hyperbolic co sine 2 Hyperbolic tangent Random number Integer random number Absolute value Smallest integer Rounding Factorial Sign Modellus Manual version 2 5 2002 ned functions Example sgrt 2 sin w t cos w t tan 5 sec 2 cosec a cotan a arcsin 0 5 arccos 0 5 arctan 0 5 In 5 log 10 sinh t cosh t tanh t rnd 10 Generates a random number between O and 10 irnd 10 Generates a random integer from 1 to 10 abs 5 int 5 3 The result is 5 round a fact 5 sign a If a lt 0 then sign a 1
11. 2 scale v 183 m 1 5 scale p 140 i 65 scale t x 37 x scale p ax 0 20175 if i then x x0 j if 1 gt 1 then x 2x0 x ax x t il 7 if 1 gt 11 then vx 4axx t 17 89 SAMPLE FILES File Modellus Manual version 2 5 2002 c Program files modellus 2 5 tutorial 09 analyzing a photo of a refraction mdl t s Modellus C Modellus 2 5 tutorial 09 analyzing a photo of a refraction mdl File Edit Case Window Help Interpret abs x n 1 38 angle i 31 57 angle r 222 32 angie i aretan abs 7 y 83 00 sin angle i angle y arcsin n Bx radius xsin angle 7 Bx 37 98 By radius xcos angle 7 Try to move point x y on the rig right Why Measure angle radius 100 51 abs x angie i arctan abs 1 sin angie i angle r aresin n Bx radius xsin angie r By radius xcos angie r 90 Modellus Manual version 2 5 2002 SAMPLE FILES File c Program files modellus 2 5 waves transversal versus longitudinal mdl is Modellus C Modellus 2 5 waves transversal versus longitudinal mdl File Edit Case Window Help 0 Axsi x t 9 x0 A xsin w xt 3 size 730 v 50 00 lambda 180 00 delay 0 20 delay 0 20 Min 0 00 Max 0 50 t 16 90 4 sui 11111 UIIMMIT EE ETT EET TIL T Hongttudinat wave ra a Transversal wave Hor 3 07 Ver
12. erties of an object in ion window 1 Click on the particle with the RIGHT button Hodellus o E dit object Car Ls Modellus NIME i 2 Edit object v 2 Answer Yes or No to choose which object to edit SEER ff M Name 7 Value v Axis Scales I Trajectory of the horizontal coordinate of the particle to 0 5 Track every steps cime Object Panic s mmm s Cancel Delete Release 4 Click OK and run the model it j i ci i E ESSA Iii P ES STR Jai 26 Modellus Manual version 2 5 2002 E W Animation 1 Cases E 1 Click on the Level Indicator button Max 20 00 BHE 2 Click anywhere in Min 0 00 the Animation Window LevelIndicator E Indicator 3 Select the E Orientation Vertical variable v to be C Horizontal displayed in the level indicator or bar NM M Value Limits 4 Set the maximum to 20 5 Click OK and run the model 27 Modellus Manual version 2 5 2002 ne nalog meter in the 1 Animation 1 n E 1 Click on the Analog Meter button ISHEBISDZUM Min 0 00 Max 10 00 2 Click anywhere in the Animation window Analog Meter NNN Meter PLESS Variable 1 1 T S f Clock C Protractor Pointer E 4 M Name M Value Background EH Limits 3 Select the variable v to be displayed in the level indica
13. select the appropriate variable in the Vertical list box If you want to change the default name Modellus assigns to the object type a new name in the Name text box Giving objects meaningful names is particularly useful when you decide to join objects Geometric Object x C Segments Polygon Circle M Value Line Thickness 1 F Points M Axis HORIZONTAL VERTICAL Scales Filled 1Pixel 1 1Pixel 1 I Trajectory Tracking Origin Var Axes gt Var Axes gt No of points Colour mu Name Object no 50 Attributes M Name Track every steps Cancel Delete 85 Modellus Manual version 2 5 2002 REFERENCE 18 To specify Name label Value labels Axis Fill for polygon or circle Trajectory Tracking which causes Modellus to display a trail of image frames at the interval you specify bject properties III Do this Toggle the Name attribute checkbox to show or hide the names of variables Toggle the Value attribute checkbox to show or hide the values of variables Toggle the Axis attribute checkbox to show or hide the object s axes Select the Filled attribute Filled is an option for polygons and circles However when you add points segments and lines Filled is selected by default Toggle the Trajectory attribute checkbox to show or hide the object s trajectory Click the Tracking checkbox Type the number of
14. Animation many of the features of Modellus You can read Help them and follow the Introduction syntax Reference instructions am Control Window Madellus Files and Imported Images and Videos Password Protection 2 The second part of the Help ESSERE Hong MUI apatia file is a hypertext Hates Windor Graph Window manual The initial Table Window Animation Window sections are concise and Properties of Animated Objects in the Animation Window N Measurement Tools in the Animation Window direct and the final sections Model Syntax are more complete The Syntax Reference section is useful for a quick check of the syntax of a E Modellus 2 5 i gt A function or of a conditional SE Bark Fonemi Hime statement D Modellus SI Workshops and Help Version 2 5 20 TH 3 Use the Show button to Modellus 2 5 look for a specific word on a gt A the Search tab or topic pm aa Index tab Contents Index Search Modellus Type in the keyword to find YR Workshops and Hel IT Md Workshops Select Topic to display Exploring Graphs Simple Oscillation with Fun Velocity and Acceleration 5 Analysing a Graph of Experi 34 Modellus Manual version 2 5 2002 RMEDIATE Modellus Manual version 2 5 2002 blank page 36 Modellus Manual version 2 5 2002 INTERMEDIATE lel syntax 1 You can open only one Model window at a time 3 A model may have variables funct
15. E lt jm gt Options soi Lei Two body problem Max 10 00 Max 50 00 s DI Min 1 00 m1 1 00 Min 1 00 geometry dy z Kinematics ma F2lx 104 Modellus Manual version 2 5 2002 SAMPLE FILES a vector File c Program files modellus 2 5 velocity mdl t x Modellus C Modellus 2 5 vdt VELOCITY MDL Ee Velocity is a VECTOR Run the model and drag the green ball 105 Modellus Manual version 2 5 2002 blank page 106 Building and exploring mathematical models is a fundamental task in science Modellus offers students and teachers a minds on multilevel learning experience in which they create simulate and analyze models interactively on the computer either from experimental data and images or from pure theoretical thinking A new scientific truth does not triumph by convincing its opponents and making them see the light but rather because its opponents eventually die and a new generation grows up that is familiar with it Max Planck
16. Info mur Highlight ud Modellus Interactive Modelling with mathematics Modells About Reviews Tutorials PDF brochure 731 Kb Examples Downloads Publications Links Join group medellus amp mail fct unl pt Last update Wednesday October 02 2002 Examples and worksheets from the Advancing Physics course Institute of Physics UK available here Modellus can be used freely for any educational purpose It cannot be sold in any condition Distribui o gratuita em m apoio do Departamento ecund rio Minist rio da o 9 Modellus Sec o de Ci ncias e Tecnologias da Educa o e da Forma o Faculdade de Ci ncias e Tecnologia Universidade Nova de Lisboa Portugal ie AY Modellus Manual version 2 5 2002 blank page Sample files images and videos Introduction Basic Installing and launching Windows and menus Writing and running a model Creating new windows and viewing multiple representations of a model Control window Viewing multiple cases Creating an animation Creating a vector in the Animation window Linking a vector to a particle Editing the properties of an object in the Animation window Creating a level indicator in the Animation window Creating an analog meter in the Animation window Creating and editing a graph in the Animation window Creating a digital meter in the Animation window Inserting images in the Animation window Inserti
17. accessible with ALT keys shortcuts Cut Copy Paste text and Undo have direct shortcuts Ctrl X Ctrl C Ctrl V and Ctrl Z in the Model and Notes windows 45 Modellus Manual version 2 5 2002 INTERMEDIATE onditions window 10 All data in the Initial Conditions window must be numeric Initial Conditions Parameters Separator bar Initial values If necessary use the separator bar to resize the window space available for the parameters and the initial values Independent variable 3 If a number appears as 0 00 and its value is for example Limite 0 004 it is necessary to change the number of decimal d Min Max 20 places in the output using the Options button of the e p Control window This change is also valid for all output Angles Graphs Tables and Animations v Degrees C Hadians Output Decimal places Formats all numbers in the P 2 Initial Conditions window Exponential threshold and in the output windows Model type Graph Table and Iterative Animation Auto Run on Open Cancel 46 Modellus Manual version 2 5 2002 INTERMEDIATE 11 The Notes window can be used to register comments and or write instructions to use the model SI This is a comment in the Notes window When the model is protected by a password the user can t change the content of the window but can copy it The maximum number of characters in the wind
18. dialogue box to change graph Limits properties HORIZONTAL Min 6 Max 26 VERTICAL Min 26 Max 26 Use the Automatic scale check box to turn the automatic scale on and off When Automatic scale l Equal scales selected the graph auto adjusts This check Iv Projection lines Points box is unselected after zooming in a graph Tangent lines when replaying Projection lines show or hide dotted lines to axes N N Tangent lines when replaying show or hide tangents in the graph c m when the replay button amp in the Control window is pressed a Egual scales force a mono metric scale 1 Points switch the graph between points and lines N ani Options The Limits box is useful for displaying specific parts of a graph To change the position of the origin the intersection of the vertical and horizontal axes in the window double click on the graph Double clicking causes the origin to move to the mouse position Cases B B Vertical To magnify a region of the graph you can zoom in the region of interest Press the left mouse button while dragging over the region you want to see more closely When the bounding box that appears encloses the region you want to magnify release the mouse button To return the focus to the view you had before you zoomed in click the Adjust button when you use the zoom feature Modellus turns off automatic scaling T
19. objects in the ation window pi 18 Use this tool To add Particle Image ball particle rectangle or referential Vector with or without arrow resultant or components Vector Vertical or horizontal slider bar Level Indicator Analogue Meter Gauge clock or protractor meters B m s Plotter Interactive plotter for drawing line or point plots IS Digital Meter Digital meter with or without the name of a variable Image Importer Bitmap image BMP or GIF format is Text Text with the colour font style and size that you specify Geometric Object Lines and shapes such as circles and polygons b 54 Modellus Manual version 2 5 2002 INTERMEDIATE E a S in the Animation 19 When changes in the values that control an object s position are very small they may not show up in the animation To make small changes in values visible in the Animation window modify the scale factor For example to magnify the effect of a change by a factor of 20 specify a scale factor of 0 05 If the range in values is very large for example from O to 500 then enter a scale factor of 5 to display the range Animation 1 x tao different scales in the coordinate and 73 00 In the graph of x as a function of time gt Elik au Plotter ES Plotter EZ HORIZONTA DO FR Name VERTICAL Attributes HORIZONTAL VERTICAL Attribu
20. re adding segments define their points in the Points Definition dialog box that appears and then click OK If you re adding a polygon define its points in the Points Definition dialog box that appears and then click OK If you re adding a line define two points on that line in the Points Definition dialog box that appears and then click OK Geometric Object x No of points Name Object no 50 M Name M Value M Points M Axis Filled l Trajectory Polygon Circle Colour mu C Line Thickness 1 HORIZONTAL YERTICAL Scales Origin Tracking Var Axes Var Axes gt Track every 10 steps Cancel Delete 84 Modellus Manual version 2 5 2002 REFERENCE 17 To specify Object type Number of points Colour Thickness of the line segments that draw the shape The scale of the object s horizontal or vertical movement on the screen The variable that controls the horizontal position of the origin of the object s axis The variable that controls the vertical position of the origin of the object s axis Object s name ject properties II Do this Select Points Segments Polygon Circle or Line Choose a number from the pop up menu Choose from the Colour pop up menu Choose from the Thickness pop up menu Type a value in the appropriate Scale text box Under Origin select the appropriate variable in the Horizontal list box Under Origin
21. the right button When a tool is edited its scale and Colours colour can be changed Text Text background E E Cancel Delete M Value Measures coordinates x y N Measures distance NS Measures distance over path Measures area M Measures slope ts Measures angles Edit to toggle between degrees and radians P 59 Modellus Manual version 2 5 2002 blank page 60 Modellus Manual version 2 5 2002 ADVANCED Modellus Manual version 2 5 2002 blank page 62 Modellus Manual version 2 5 2002 ADVANCED B g derivatives a 1 To compute a first order derivative or a partial derivative of a known function the function must precede the derivative Derivatives are computed symbolically In the following example dx H di X 2xX u dx dt is not parsed as a derivative and yields two new variables dx and dt The correct syntax is k 2Xf N di To compute a derivative or a partial derivative of expression y with respect to variable x the variable x must be explicitly stated in expression y In the following example v 2Xd y x AV dx z dy dx is treated as a derivative and yields z which eguals 1 However z dy da will not parsed as a derivative and yields two new variables dy and da 63 Modellus Manual version 2 5 2002 ADVANCED tial equations 2 Write differential equations as in
22. version 2 5 2002 INTERMEDIATE Window structure 15 To create an animation choose New Animation from the Window menu Notice that as you move the mouse over tools and buttons Modellus gives you helpful tips at the bottom of the window You can open up to three Animation windows per model A Animation 1 Ea IE EEB E Cocada Tools to make measurements A Tools to create animated Grid on off objects Background button gt 8 0 mit Measure slope The left buttons are used to create objects in the animation controlled by the variables The top central buttons are tools for making measurements from still images GIF or BMP or video AVI which can be placed in the background using the background button A grid can be switched on and off using the grid button Clicking the background button you can define the grid spacing and colour as well as the background colour 51 Modellus Manual version 2 5 2002 INTERMEDIATE 16 A grid is very helpful for Background E positioning objects Attributes precisely To define the grid Colour gt C Grid Spacing pixels click the Background button Stars to open the Background Clmagefvideo QU o Browse dialog box where you define the grid 3 cm Choose a colour for the grid lines from the Grid colour pop up menu TI Animation 1 O P e D El Specify the spacing between grid line
23. 07353 fh 0 351906 semi 12 669000 40 _ 60 Time s RC 15 000000 V0 1 412 semi 12 669 F FOxe k x t AC 1000 x 1086 x 15000 99 SAMPLE FILES 12 File Modellus Manual version 2 5 2002 an motion c Program filesimodellus 2 5 brownian motion mdl x Modellus C Modellus 2 5 brownian motion mdl File Edit Case Window Help x lastx rmd 10 rnd 10 Y 7 last rnd 10 rnd 10 gt 2 P VlxX ty x E Animation 1 na Cases E d2 last d2 G2 last X nitial Conditions gt 535 34 54 53 530 45 45 93 542 82 20 62 550 81 45 93 560 65 56 65 514 14 97 26 526 38 111 86 509 58 45 63 524 56 49 18 522 51 513 16 I 7 s last X re y last W X last X rnd 10 rnd 10 Y lastY rnd 10 rnd 10 X2 last x rnd 10 rnd 10 2 lasty2 rnd 10 rnd 10 100 Modellus Manual version 2 5 2002 SAMPLE FILES File c Program files modellus 2 5 oscillation from a video mdl Modellus C Modellus 2 5 oscilation from a video mdl 18 xl Control t 3 000000 0 4 mmm DEC 360 x A xcos xt 180 T 1 step 15 15 frames s step 0 066667 A 42 000000 T 2 000000 360 x74 Xcos xf 180 101 Modellus Manual version 2 5 2002 SAMPLE FILES 14 File amical reaction c Program files modellus 2 5 chemical reacti
24. 2002 CD ROM contents Install Modellus E Modellus 2 5 Manual ti Modellus Website Acrobat Reader 5 05 amp Modellus Library Pasco Videos Photos for data Analysis Data from Sensors Images for Animations Faculdade de Ci ncias e Tecnologia Universidade Nova de Lisboa 2002 E Modellus 2 5 O e gt fa Show Back Forward Home Modellus Workshops and Help Version 2 5 2002 Workshops Exploring Graphs simple Oscillation with Functions Velocity and Acceleration with Differential Equations Analysing a Graph of ermental Data and Creating an Animation Help Introduction evntax Reference Basics Model Window Control Window 1 odellus Files and Imported Images and Videos Password Protection Common Buttons and Shortcuts Initial Conditions Window Notes Window Graph Window Tahle Window Animation Window Properties of Animated Objects in the Animation Window Measurement Tools in the Animation Window Model syntax launching 1 Place the CD with an auto run for the index htm file select the link Install Modellus and choose the version you want to install 2 Use preferably the directory c Program files modellus as the destination folder 3 A Modellus file can be launched from the file with a double click only if Modellus is not running 4 A Modellus file can also be launched from a link in an HTML browser only if Modellus is not running Wher
25. 35 41 airplane moving airplane not moving airglane moving V plane ground 300 08 without wind ficating in the air with wind with wind Tipler p 73 problem n 27 A plane flies at a spead of 250 km h relative to still air There is a wind blowing at 80 km h in the northeast direction that is at 45 to east of north a In what direction should the plane head so as to fly due north b What is the speed of the plane relative to the ground Solution west of north by 13 1 b 300 km h v wind xsin angie wind angie piane N arcsinl v piane vx wind v wind xcos angie wind vy wind v wind xsin angie wind vx piane v_plane xsin angle plane N vv piane v piane cos angle plane N y plane plane x t x plane vx plane x t x wind vx wind t y wind vy wind x t v plane ground v piane x cos angle plane N v wind xeos 45 96 SAMPLE FILES Modellus Manual version 2 5 2002 c Program files modellus 2 5 tutorial 14 boat crossing a river with differential equations mdl Modellus C Modellus 2 5 tutorial 14 boat crossing a river with differential equations mdl E E m laj x File Edit Case Window Help Animation 1 97 10 x dx yx boat vx river dt a yy boat vy river dt vx vx boat vx river Vy wy boat vy river dx river yx river dt dy river 7 yy river dt vy boat if vx boat
26. 70 then angie atan vx boat vy boat if vx boat lt 0 then angle atan 180 vx boat Ax 10 xsin angie Ay 7 10 x cos angle Bx Ax 20 xcos angie By Ay 20 xsin angie Cx By Bx x2 Cy Bx By x2 Ex 7 10 xsin angie Ey 10 cos angie Dx Ex 20 x cos angie Dy Ey 20 xsin angie Modellus Manual version 2 5 2002 SAMPLE FILES 10 File c Program files modellus 2 5 tutorial 10 an oscillation from data mdl x Modellus C Modellus 2 5 tutorial 10 an oscillation from data mdl File Edit Case Window Help Copia 2d 3 5 scale t 0 9 scale p Nm Animation 1 Dj x LES 1 22 60 wh p scale p 0 00457 scale t 0 01036 282 T x scale t 1 0 24402 30 00000 N xm 7119 x scale p i 7 phased 36 86990 A 0 13706 T 1 46006 A mass oscillating on a spring Time s Finding the model of this oscillator Measure angle 3 5 scale t 338 0 0 60 x scale p xm 119x scale p 18 phase arcsin 30 360 x A sin X t phase xm T 98 Modellus Manual version 2 5 2002 SAMPLE FILES 11 File c Program filesimodellus 2 5 decay capacitor data mdl ix Modellus C Modellus 2 5 decay capacitor data mdl File Edit Case Window Help gt teeraa le LEE Control EJ t 9250000 0 120 lt mmm am Jum DOG 0 E ortone fv 0 0
27. In this case the image grows outward from its centre To specify The variable that controls the image s horizontal size Do this Select it in the Horizontal list box The variable that controls the image s vertical Select it in the Vertical list box size The variable that controls the horizontal position of the origin of the image s axis Under Origin select the appropriate variable in the Horizontal list box The variable that controls the vertical position Under Origin select the appropriate variable of the origin of the image s axis in the Vertical list box Image Importer Lx HORIZONTAL VERTICAL Name Ui Goes Attributes Name M Value Change scales Origin Var Axes gt Var Axes bd Image fram file Cancel Delete amp Position Size from lower left C Size from center 81 Modellus Manual version 2 5 2002 rter properties IV Properties not affected by variation To specify Do this Image Type or browse for the name of the image file to import Modellus imports the image by reference Any change to the pathname you specified when the image was imported will break the link to the referenced file Image s name If you want to change the default name Modellus assigns to the image type a new meaningful name in the Name text box Name labels Toggle the Name attribute checkbox to show or hide labels such as the names of variables Value label
28. M Arrow Tracking Scales Origin Var Var Track every steps View C Components Resultant Name Colour muu Thickness 1 Ed Cancel Delete Helpase 73 Modellus Manual version 2 5 2002 To specify Name labels Value labels Axis Vector with an arrow Tracking which causes Modellus to display a trail of image frames at the interval you specify Representation of vector Do this Toggle the Name attribute checkbox to show or hide labels such as the names of the vector s components Toggle the Value attribute checkbox to show or hide labels such as the values of variables that control the vector Toggle the Axis attribute checkbox to show or hide the vector s axes Select the Arrow attribute Click the Tracking checkbox Type the number of steps in the text box Tracking is associated with the time step specified in the Control Options dialog box Each image frame in the track is eguivalent to a time step For example if the time step is set at 0 1 and you specify tracking at every 10 steps then Modellus will show one image per second Select Components to represent the vector as its components HORIZONTAL VERTICAL Name 0 const Attributes M Name M Value M Axis M Arrow Tracking Scales Origin Var Axes F Axes gt Var Colour muu Thickness 1 Track every steps View C Components amp Resultant C
29. Modellus can also be used as a tool to analyse and make sense of experimental data providing tools to make models from images photos graphs etc in BMP or GIF format and videos AVI format Modellus can be integrated in any elementary course of mathematics or physical sciences or in any advanced course that makes use of functions differential equations iterations etc Users can Select ready to use models from the library of models that come with Modellus or download them from the web page Quickly customize existing models to meet specific needs Create their own library of reusable models Preserve the integrity of models by password protection Modellus gives teachers and students a powerful technology for learning mathematics and science at secondary school and college level 11 Modellus Manual version 2 5 2002 blank page 12 Modellus Manual version 2 5 2002 To create a world and watch it evolve is a remarkable experience It can teach one what it means to have a model of reality which is to say what it is to think It can show both how good and how bad such models can be And by becoming a game played for its own sake it can be a beginning of purely theoretical thinking about forms Jon Ogborn 13 Modellus Manual version 2 5 2002 blank page 14 Modellus Manual version 2 5 2002 15 Modellus Manual version 2 5 2002 blank page 16 Modellus Manual version 2 5
30. a hyperlink if and only if Modellus is not running GIF and BMP images can REM BEE be used in the Animation window In the background of the Animation window it can be placed a GIF or a BMP Horizontal image or an AVI video An Adjust AVI video appears asa L dl O Model int eted Hor 56 30 Vert 81 63 Double click to set origin Cli A 3 duplicate image the left ECCO Tsjo is the origina video where nothing can be placed over it The right is a copy of the left image where annotations and measures can be made TET ST mtt It is recommended to keep these external files in one or more folders on the Modellus folder The File menu has an option Preferences where these folders can be specified as default folders for images This will make it easier to Modellus to locate the files if any Preferences ET path name problem arises Default Folders Images Videos videos photos images sensors Use to separate foldersipaths of images and videos 8 characters maximum per folder name 42 Modellus Manual version 2 5 2002 INTERMEDIATE age masks Some of the images used with Modellus are accompanied by a second image with a similar filename but with the letter m tagged onto the end of the filename For instance a filename ball gif can be accompanied by a filename ballm gif Modellus reads the second file as a mask file Mask files en
31. able you to mask away portions of a picture that you want invisible To find out more about masks read a computer graphics reference book Example of an image with a mask ballm gif ball gif A sequence of images with names like natal bmp natall bmp natal2 bmp etc can be used to animate an image when file natal gif is placed in the Animation window as a particle natal bmp 4 natal1 bmp 4 natal2 bmp 4 43 Modellus Manual version 2 5 2002 INTERMEDIATE m d protection E AD LE A Vil 1 W eo A 8 To maintain simulation and experimental integrity or to hide certain details from students or other users you can protect a model by giving it a password Before assigning the password you can hide or display the Model window and or visual representation windows so that users see only what you want them to see Users cannot open or hide any window after the password is assigned Users cannot close any windows that are displayed after the password is assigned For example if you want the users of your model to see it represented as an animation and a graph but not as an eguation hide the Model window before you assign a password To assign a password choose Password from the File menu Confirmation m Type the password in both text boxes Keep in mind that the password is case sensitive Click OK Save the model You also use the Password command to remove password protection from a previo
32. ancel Delete Helpase 74 Modellus Manual version 2 5 2002 REFERENCE El To specify The variable that controls movement in the level indicator Colours for the level indicator when full and when empty Orientation Name labels Value labels Values that limit the range of movement from one end to the other A value within the limits specified that determines the level indicator s increment licator properties Do this Select it in the Variable list box Choose a colour from the appropriate pop up menu Select Vertical or Horizontal Toggle the Name checkbox to show or hide the names of variables and the Min and Max labels Toggle the Value checkbox to show or hide the values assigned to variables and the Min and Max labels Enter a value in the appropriate Limits text box The defaults are O for Minimum and 1 for Maximum Enter a value in the Step text box For example to increment values by 1 specify 1 as the Step value To increment by 2 specify 2 To report intermediate values specify O LevelIndicator E Indicator LevelIndicator E Variable Orientation amp Vertical Horizontal M Name Value 75 Modellus Manual version 2 5 2002 REFERENCE neter properties 8 To specify Do this The variable that controls the Select it in the Variable list box pointer s movement in the meter Colours for the pointer and the Choose a colour f
33. ar To add an object click a tool in the toolbar Then click in the Animation window to position the object where you want it to appear When you move the mouse pointer into the window the pointer changes to together with a picture of the tool you re using As soon as you release the mouse button Modellus defaults to the Pointer Edit tool and displays a properties dialog box In the object dialog box specify properties such as variable assignment colour or type for the object you re adding When you click OK or Cancel the object appears in the Animation window With the exception of text the objects you add to an animation function as output devices by default Output devices display values reported by the simulation You can use an object as an input device by assigning to it a parameter that you can interactively alter during simulation To open an object s properties dialog box right click an object To delete an object click Delete at the bottom of the object s properties dialog box To duplicate an object drag it with the Ctrl key pressed except for Geometrical Objects When the Pointer Edit tool is active you can reposition objects in the Animation window or resize level indicators analogue meters and text using the left button Reposition pointer Min 10 00 Max 10 00 Resize pointer a 5 00 man Mir 10 00 Max 10 00 55 Modellus Manual version 2 5 2002 INTERMEDIATE n nimated
34. at every 10 steps then E E D const t Attributes Modellus will show one image per x M Name second M Value M Axis Trajectory Tracking Track every steps Cimage 2 10 6 Object Paice s Em s Cancel Delete Release 72 Modellus Manual version 2 5 2002 To specify The variable that controls the magnitude of the vector s horizontal component The variable that controls the magnitude of the vector s vertical component The scale of the vector s horizontal and vertical components The variable that controls the horizontal position of the origin of the vector s axis The variable that controls the vertical position of the origin of the vector s axis Colour Thickness of the vector Vector s name properties I z Do this Select it in the Horizontal list box Select it in the Vertical list box Type a value in the appropriate Scale text box Under Origin select the appropriate variable in the Horizontal list box Under Origin select the appropriate variable in the Vertical list box Choose a colour for the vector from the Colour pop up menu Choose a thickness from the Thickness pop up menu To change the default name Modellus assigns to the vector type a new name in the Name text box Giving vectors meaningful names is particularly useful when joining objects HORIZONTAL VERTICAL 0 const Attributes M Name M Value M Axis
35. cillation a Xees w x t fase0 damping a xe Ckxt xcos w x t fase 94 Modellus Manual version 2 5 2002 SAMPLE FILES File c Program files modellus 2 5 orbital 1s with random points mdl Modellus C Modellus 2 5 orbital 1s with random points mdl File Edit Case Window Help Rt AX A Ri 2441 557 xg a mime Animation ms if n Cases E AAAA Control EE j t 13780 0 5000 if 0 then rnd 250 and and p inc 4x x x72 Ris x102 and Rpis 4xx x 1 s orbital LI t ea LES a N E a A wot ected NI o Ae eh Ata t Hi N EGER PNEU TSS N e At T fi eria k dr ilc n NI t e Adi e YY f 1 5 N 2 2 2 2 2 if n 0 then rnd 250 and 7 22x a xe and p imt 4x7 xr x Ris x10 and RpIs 4x7 xp x RIs if n lt p then 7 5 1 and ang rnd 360 and x xeos ang and y 77 xsin gang if n p then 5 0 95 Modellus Manual version 2 5 2002 SAMPLE FILES tive velocity File c Program filesimodellus 2 5 wind a problem of relative velocity from Tipler mdl x Modellus C Modellus 2 5 wind a problem of relative velocity fro Tipler mdl File Edit Case Window Help v wind xsin angle wind angie plane N arcsin v piane ixi EEE y_plane 1461 10 y planez1461 10 angle plane N U x plane 339 4 x plane 3
36. dow Patile ___ Oo pmP9q9LZ 3 Select x as the HORIZONTAL YERTICAL Name horizontal EM Mollica coordinate for the alue particle Scales Trajectory mr Origin 5 Give the name Var Var Car to this reds p Ads particle in the Name box Clmage Browse Object 6 Click OK and run the model Cancel Delete Release 25 Modellus Manual version 2 5 2002 mun Animation LES es 1 Click the Vector button 2 Click anywhere in the Animation window E STR jaf s HORIZONTAL VERTICAL Name 0 const Attributes M Name 3 Select v as the N v M Value horizontal Axis component of the 7 Arrow Tracking vector Track every steps Scales 4 Changethe tl fT ae y horizontal scale to Origin Components 0 1 Var Var Resultant Colour MN 5 Uncheck Axis Thickness 3 gt 6 Change Thickness Cancel Delete Release to 3 and Colour to red 7 In the Name box write v 8 Click OK and run the model 24 Modellus Manual version 2 5 2002 ector to a particle ID Animation 1 1 Drag the tail of the vector on the particle Modellus 2 Answer Yes to the E i 2 Link to Car question Link to A Animation 1 N e in A qu in EI 3 Run the model Tihi ana kattaa aa aaah OR PR PR PR PP pra Ef S k jme 25 Modellus Manual version 2 5 2002
37. e from the pop up menu Then choose a colour for the particle from the Object colour pop up menu HORIZONTAL VERTICAL Name Object no 35 580 t i t SENI Attributes x M Name M Value M Axis Trajectory Tracking Track every steps Cmae 0 6 Object Price s En s Cancel Delete Helease 71 Modellus Manual version 2 5 2002 ject properties II To specify Do this Particle object s name To change the default name Modellus assigns to the particle type a new name in the Name text box Giving objects meaningful names is particularly useful when joining objects Name labels Toggle the Name attribute checkbox to show or hide labels such as the names of variables Value labels Toggle the Value attribute checkbox to show or hide labels such as the values on the axes of a ball s referential Axis Toggle the Axis attribute checkbox to show or hide the object s axes Trajectory Toggle the Trajectory attribute checkbox to show or hide the object s trajectory Tracking which causes Modellus to display Click the Tracking checkbox a trail of image frames at the interval you Type the number of steps in the text box specify Tracking is associated with the time step specified in the Control Options dialog box Each image frame in the track is eguivalent to a time step For example if the time i article step is set at 0 1 and you specify HORIZONTAL VERTICAL amet e a tracking
38. e to start Load the file 01 a car accel with a function mdl in the Tutorial folder Read and examine it carefully Then run it Look at model 02 derivatives mdl in the same folder And so on You can also choose Workshops and Help from the Help menu Then choose one of the four workshops Modellus Manual version 2 5 2002 Control window 3 Modellus Untitled File Edit Case Winddw Help E ECC Js EOS interret 55 Ra S eso amp es 5 L E Graph window te Adjust Options n Hor 56 30 Vert 81 63 Double click to set origin Click Model interpreted Animation 1 B inDix MEN Ea e 21 A A Animation window TET RDO mri Notes window Model window File menu Edit menu Case menu Window menu Help menu Hs EN e Window Help Add Mew Undo Workshops and Help Open jemove L tsi Teen About Modellus Save EN New Table i Copy SEP BR E Paste Standard Password EG Cascade A i E Copy Window Ta Preferences Falli d 1 Control Exit 2 Initial Conditions 3 Notes v 4 Model 18 Modellus Manual version 2 5 2002 running a model A Modellus Untitled File Edit Case Window Help Control x Model Km cu e e Mox fax si Options Mbdelinterpreked n EC Lo Hor 56 30 Vert 81 63 Double click to set origin Click Animatio
39. elength and b is 10 Stops the execution of the model when y lt 0 and the current value of t is assigned to a Pauses the execution of the model when t 5 and the current value of t is assigned to a To continue the execution press the pause button in the Control Window Pauses the execution of the model when t 5 and the value 10 is assigned to a The model is suspended for 10 time units approximately 10 tenths of a second 70 Modellus Manual version 2 5 2002 To specify The variable that controls the particle s horizontal movement The variable that controls the particle s vertical movement The scale of the particle s horizontal or vertical movement on the screen The variable that controls the horizontal position of the origin of the particle s axis The variable that controls the vertical position of the origin of the particle s axis Type of object to add image or object ject properties I Do this Select it in the Horizontal list box Select it in the Vertical list box Type a value in the appropriate Scale text box Click the Origin checkbox Under Origin select the appropriate variable in the Horizontal list box Click the Origin checkbox Under Origin select the appropriate variable in the Vertical list box If image click Image and then type or browse for the name of the file to import Modellus uses BMP and GIF formats If object click Object and then choose the object typ
40. eric Click the Font button to open the Font dialog box where you specify the font style and size for the text Name labels Toggle the Name checkbox to show or hide the names of variables Variable HORIZONTAL VERTICAL Origin Var axes Var Axes gt Scales M Name Colour mmm Font i Cancel Delete Release 78 Modellus Manual version 2 5 2002 Properties affected by variation The Variation property you select affects some but not all of the other properties you can specify The three tables that follow list the properties that Variation does affect Position Variation which is the default selection affects the image s movement in the Animation window the image s size remains static To specify Do this The variable that controls the image s Select it in the Horizontal list box horizontal movement The variable that controls the image s vertical Select it in the Vertical list box movement The scale of the image s horizontal or vertical Type a value in the appropriate Scale text box movement on the screen The variable that controls the horizontal Under Origin select the appropriate variable in position of the origin of the image s axis the Horizontal list box The variable that controls the vertical position Under Origin select the appropriate variable in of the origin of the image s axis the Vertical list box Image Importer FI HORIZONTAL VERTICAL Name Object no 47
41. ick OK and run the model 30 Modellus Manual version 2 5 2002 in the Animation Animation 1 O on ia iD n El Pn n5 D PSP PP PD PP DPPPPEI AA TRE E TT AT TT TT TT TA gt K mirit 1 Click on the Image Importer button 2 Click in the Animation Window HORIZONTAL VERTICAL Name 3 Select x as the 0 const horizontal coordinate of the image 1 Shan a i Change ge the scale ae Position of the horizontal Origin Size from lower left coordinate to 0 5 Var Axes x Var Axes Size from center Image from file 5 Select the file Browse BMP or GIF to Cancel Delete use Open file Ki x 6 Click OK and run sa E E ile name Folders the model a c XmodellusXimages Lu e cA Get C3 modellus Ey images escher 1 bmp europe gif eye gif eve gif List files of type Drives Git Empi git bmp S cc pc disk 31 Click on the Text button Click in the Animation window Write the text in the Text box Select x as the horizontal coordinate of the text Change the scale of the horizontal coordinate to 0 5 Change the colour Click OK and run the model Modellus Manual version 2 5 2002 E Animation 1 Cases s RA D PD D P PP PPPPSPPPRPi A BTATAVATATATATATRTARTATARTATRTATATA TUR particle moving with constant velocity BRE RROD Gia
42. ions differential eguations iterations and conditions Variables appear in green italic Numbers appear in regular text and portions that it interprets as function names e g sin cos etc and logical conditions if then and or appear in bold Any set of alphanumeric characters the letters a through z and the numbers O through 9 or the merda underscore character starting with a letter if 77 then x x0 e g F2 x can be used to define a variable if f gt 1 then z x0 xax x 1 17 2 Modellus is case sensitive so T is different from t if 1 gt 1 then vx ex x rz 27 By default the independent variable is t It can be changed to any other letter using the Options button in the Control window The left hand side of an equation can only have one variable E g lineor ad bxi v 2x linear In this model a and b are considered as parameters The initial values for the parameters are given in the Initial Conditions window A line can have only a name of an independent variable E g AX AV hr This is useful in many situations For example to create geometric images than can be directly manipulated 37 Modellus Manual version 2 5 2002 INTERMEDIATE 2 Addition Subtraction Multiplication or press the space bar Division To enter a fraction type the numerator followed by the slash character and then type the denominator For example ty
43. letter step Independent variable step Limits Min j0 Max Angles Independent variable limits e Radi Degrees Radians Angles in degrees or radians Output Decimal places Numbers output format Exponential threshold 3 Model type Check to create iterative Iterative models without Independent variable M Auto Run on Open Check to run the file Cancel automatically after loaded 21 Modellus Manual version 2 5 2002 x Modellus Untitled MEI EJ File Edit Case Window Help Control Print window contents Initial Con ditions i 3 i 12 00 coe Parameters case 1 case 2 case 3 Options case 1 case 2 case 3 EEG FI Jaa Ld Rd Eu 1 Choose Add 2 Give from the Case different Menu to add a values to the case The parameter v maximum number of 3 Run the model and select the cases is 5 colour of the cases you want to Use also this see In the Graph window it is menu to possible to see multiple cases delete a case simultaneously In the Table and Animation windows only one case can be seen 22 Modellus Manual version 2 5 2002 an animation Windows menu window _ New Graph NeW Table Standard Lascade Tile 1 Control v 2 Initial Conditions 3 Model 4 Notes Animation 1 1 Click the Particle button 2 Click anywhere in LO the Animation win
44. lus recognises For the best result when copying equations into another application use Copy Window Otherwise some characters might be displayed differently For example in the Model window Modellus interprets the character as pi 3 14159 However when you paste the equation into another application you ll see Inserting comments Type a semicolon at the beginning of a comment line Modellus ignores commented lines For example Consider a satellite orbitint the Earth Enter only one statement per line 39 Modellus Manual version 2 5 2002 INTERMEDIATE EW a ed functions and Imaginary numbers 4 Pre defined functions and conditional statements appear in bold logarithm log x sine sin x if 1 lt 1J then x x0 5 if gt 7 then x x0 xaxx t 11 7 For a complete list of the pre defined functions and conditional statements see the Reference section of this manual or the Modellus help file Imaginary numbers When Modellus finds an imaginary number in any variable it does the following e When the variable appears in a Graph window Modellus does not plot the number e When the variable appears in an Animation window Modellus displays the number like this y e When the variable appears in a Table window Modellus displays the number like this Table 1 Cases El 1 00 al 0 62 Modellus Manual version 2 5 2002 INTERMEDIATE gt
45. n 1 nix Parameters Initial values case 1 1 Write the model 2 Press in the Model Interpret window Use or the space bar to get the multiplication operator The Initial Conditions 3 Give a value 4 Run the model The window appears when to the independent variable t there are parameters or parameter has domain 0 20 units initial values v All values in this window must be numeric 19 Modellus Manual version 2 5 2002 windows and viewing entations of a model Window menu E Graph m namn Cases BH New Animation Vertical Mew Table Standard Lascade Tile 1 Control 2 Initial Conditions 3 Notes v 4Model Horizontal Press Adjust to fit Ke the graph mete Hor 4 09 Vert 53 Double click to set origin Click and di 4 00 8 00 12 00 16 00 20 00 24 00 Window E Table 1 New Graph New Animation stan ard Cascade Tile i 1 Control 2 Initial Conditions 3 Notes 4 Model we 5 Graph 1 Drag or Ctrl Click to select variables Selected va aber es 20 Modellus Manual version 2 5 2002 window gt 4 Control window Symbol and current value for the independent variable Control Replay pause Go to last calculated value One step One step Go to first value backward forward Stop Drag to browse in the domain Run pause Independent variable t Independent variable
46. ng text in the Animation window Creating a geometric object in the Animation window Getting help Intermediate Model syntax Mathematical operators Editing equations and inserting comments Pre defined functions and conditions Imaginary numbers Control window Modellus files and imported images and videos The Preferences dialog box Image masks Password protection Common buttons and shortcuts Initial Conditions window Notes window Graph window Options in the Graph window Zoom and copy Table window Animation window structure Animation window grid and background Adding moving and editing objects in the Animation window Types of animated objects in the Animation window Scale factors in the Animation window 7 11 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Modellus Manual version 2 5 2002 Attaching objects and releasing attached objects 56 Copying animations 57 Interacting with objects in the Animation window 58 Measurement tools in the Animation window 59 Advanced 61 Computing derivatives 63 Differential equations 64 Iterative models 65 Reference 67 Pre defined functions 69 Conditions 70 Particle object properties I 71 Particle object properties II 72 Vector properties 1 73 Vector properties 1 74 Level indicator properties 75 Analog meter properties 76 Plotter properties 77 Digital meter properties 78 Image impo
47. o copy the entire contents of the Graph window as an image and paste it into another application choose Copy Window from the Edit menu or click the copy button at the top right of the Graph window The graph is pasted with the names of the variables near the axes 0 00 24 00 20 00 49 Modellus Manual version 2 5 2002 INTERMEDIATE able window 14 To view the model as a table choose New Table from the Window menu You can open up to three Table windows per model Notice that Modellus gives you helpful information at the bottom of the window To select several variables at once hold down the Control key while you re selecting In the following illustration a column of values appears for each variable selected EI MIEN 0 00 O00 a 0 10 0 52 EA Table 1 Cases M 0 20 1 05 0 30 1 56 0 40 2 06 0 50 2 90 0 60 2 09 1 70 3 58 0 50 4 07 0 90 4 54 1 00 5 00 1 10 5 45 00 o Copy window contents to the clipboard Click the Case buttons at the top left of the Table window to view the data sets you specified for various parameters You can view one case at a time To copy data from a Table window and paste it into an application spreadsheet word processor etc choose Copy from the Edit menu or click the copy button at the top right of the Table window The data appears in columnar format with the variable name at the top 50 Modellus Manual
48. on cyclopropane propene mdl k 0 040 cyclopropane gt propene at 500 mm Horizontal Adjust Options PIERINO mr P_50E1 1 25E1 g s fi m Cyclopropane C3H6 gt Propene C3H6 0 i m DEEDS time in min K in miri 102 Modellus Manual version 2 5 2002 SAMPLE FILES 15 File c Program files modellus 2 5 tutorial 13 interactive regression line mdl 1 Modellus C Modellus 2 5 tutorial 13 interactive regression line mdl File Edit Case Window Help bm E JAHH ES RE sumx xl x2 x3 x4 x5 gt Done ais sumy yl y2 y3 y4 y5 Run the model and then move points Look how it affects the slope and the intercept of the regression line sumx xI x2 x3 x4 x5 sumxy x X y x2 xy2 x3 X y3 xd x yd x5 x yo Lad 2 dt sumxg xl tx x3 x4 y 2 al 2 J af sumyg yl ty y3 e y SILMIN WALAN y SUMY SUMY 7 N x sumxg sumx intercept ymean slope xmean N X sumxy sumx X SUMY F 2 2 N x sung sumx NI AN x sumyg sum eixo 120 xx30 70 JITxx50 intercept slope x xx50 103 Modellus Manual version 2 5 2002 SAMPLE FILES body problem 16 File c Program filesimodellus 2 512 body problem interactive mdl Modellus C Modellus 2 512 body problem interactive mdl A xl File Edit Case Window Help Aara geomet
49. ow is about 3200 about 2 pages You can copy text to and from the Notes window using the Edit menu or the shortcuts 47 Modellus Manual version 2 5 2002 INTERMEDIATE 12 A Graph window can show any variable or parameter as graph To view the model as a graph choose New Graph from the Window menu You can open up to three Graph windows per model Model a JE JE JL Los Hes luo x 7 xsin w xt Graph 1 werk aa S vertical x 2000 24 00 Initial Conditions Horizontal Ie m A djus t Parameters n case 1 case 2 Options Hor 25 26 Ver W case 3 Initial values case 1 case case 3 The variables are selected in the Vertical list box To choose more than one variable drag the mouse over adjacent variables To choose non adjacent variables use Ctrl click The Horizontal combo box lists the horizontal variable By default the selected variable is the independent one but any variable can be chosen The coloured buttons cases H oO O allow the selection of one or more cases Colours match the different cases not variables The Adjust button automatically adjusts the scales for a best fit in the available space for the current domain and counter domain The Options button opens a dialogue box to change graph properties See next page 48 Modellus Manual version 2 5 2002 INTERMEDIATE 13 The Options button of the Graph window opens a
50. pe 2 P T to enter the fraction 2x P T i If the numerator or denominator is an expression enclose the expression in parentheses Tool palette Exponent 2 If the argument of the square root is an expression enclose the expression in Square root j parentheses Requires a variable not an expression To compute the rates of change of two variables divide the change in one variable by the change in the other variable Delta x change in x Yo Non defined value for x Ex e F Elle Last value of x i Requires a variable not an expression If the argument of the square root or of the exponent is an expression enclose the expression in parentheses For example type displ dispx 2 dispy 2 to enter 7 m dispi dispx dispy d 38 Modellus Manual version 2 5 2002 INTERMEDIATE E E i uations and inserting 3 Editing equations Use the standard keys for editing Backspace Delete Home End and arrow keys If you make a mistake and want to start over you can clear the Model window of its contents by choosing New from the File menu Copying and pasting Use the Cut Copy and Paste commands on the Edit menu to cut copy and paste equations within the same model from model to model or into another program You can also copy an equation you typed in a word processing application and paste it into the Modellus Model window as long as the equation contains the characters that Model
51. rom the appropriate pop up menu background Minimum and maximum limits for Type a value in the appropriate text box amplitude The defaults for Gauge are O and 1 the defaults for Clock are O and 60 The defaults for Protractor are O and 360 if angles are measured in degrees or O and 6 28 if angles are measured in radians A value that regulates the Enter a value in the Step text box pointer s movement within the For example to increment values by 1 specify 1 as limits specified the Step value To increment by 2 specify 2 To report intermediate values specify O Name labels Toggle the Name checkbox to show or hide the names of variables and the Min and Max labels Value labels Toggle the Value checkbox to show or hide the values assigned to variables and the Min and Max labels Meter type Select Gauge Clock or Protractor Yariable t z x G v C Clock C Protractor Pointer TEN gt Name M Value Limits Background E Cancel Delete 76 Modellus Manual version 2 5 2002 To specify The variable that controls the plotter s horizontal movement The variable that controls the plotter s vertical movement Horizontal or vertical scale Colour for points or line Thickness of points or line Name labels Value labels Axis Pencil Projection lines Points Line E roperties Do this Select it in the Horizontal list box Select it in the Vertical list box
52. rter properties I 79 Image importer properties II 80 Image importer properties III 81 Image importer properties IV 82 Text properties 83 Geometric object properties I 84 Geometric object properties II 85 Geometric object properties III 86 A sample of the sample files 87 Computing acceleration 89 Refraction 90 Waves 91 The relativistic Doppler shift 92 Free fall 93 Functions 94 1s orbital 95 Wind and relative velocity 96 Boat in a river 97 Oscillation 98 Decay 99 Brownian motion 100 Pendulum 101 Chemical reaction 102 Regression line 103 Two body problem 104 Velocity is a vector 105 Modellus Manual version 2 5 2002 Sample files images and videos The Modellus sample files have been provided by many colleagues Most are identified with the author s name except those created by Modellus authors The video files are used with permission from Pasco Scientific http www pasco com and VideoPoint http www lsw com videopoint CD ROM contents Install Modellus 48 Modellus 2 5 Manual ti Modellus Website Acrobat Reader 5 05 amp Modellus Library You can browse the images and video files ja Pasco Videos Photos for data Analysis following the appropriate links on the Modellus Rata renkaat images for Animation CD Faculdade de Ci ncias e Tecnologia Universidade Nova de Lisboa 2002 Data from Sensors Click to see an image in 1 1 size Use the right button to save an image on a folfer
53. s Toggle the Value attribute checkbox to show or hide labels such as the values of variables Image Importer FI HORIZONTAL VERTICAL Name AB O const Attributes Name M Value Change scales Origin Var Axes bd Var Axes Image from file Cancel Delete Position C Size from lower left Size from center 82 Modellus Manual version 2 5 2002 To specify The variable that controls the horizontal location of the text s origin The variable that controls the vertical location of the text s origin The scale of the text s vertical or horizontal movement on the screen Do this Under Origin select the appropriate variable in the Horizontal list box Under Origin select the appropriate variable in the Vertical list box Type a value in the appropriate Scale text box Font Colour MM HORIZONTAL VERTICAL Origin Var Var Scales Cancel Delete Release 83 Modellus Manual version 2 5 2002 c object properties I In the Geometric Object properties box follow these general steps e Specify the object to add by clicking the appropriate Type If you re adding points choose the number of points from the pop up menu and define their location in the Points Definition dialog box that appears and then click OK If you re adding a circle define its centre and another point in the Circle dialog box that appears and then click OK If you
54. s by typing a value in the Spacing text box You can switch the grid on and off by clicking the Grid button at the top of the Animation window To specify the background for the animation click the Background button In the dialog box that appears select one type of background Colour Image Video or Stars To specify a colour choose from the Colour pop up menu To specify an image BMP or GIF files or a video AVI file type or browse for the name of the image file to use n a m u FA E H W m n E Cia i m ag RTH HH di 4i an a n E a a BEEP i R momentum after ye after Modellus imports the image by reference Any change to the pathname you specified when the image was imported will break the link to the referenced file Note If you want to use an image or a starfield as background choose these after you ve finished with the grid When the grid is on Modellus turns off stars and image backgrounds and defaults to a colour background 52 Modellus Manual version 2 5 2002 INTERMEDIATE ng and editing objects Animation window 17 Use the toolbar on the left side of the window to add objects to the animation When you move the mouse over a tool button a tip about that tool is displayed at the bottom of the window Modellus default is the Pointer Edit tool except when you click another tool in the toolb
55. stantaneous rates of change equal to some expression variable or parameter For example dx vx di aw 5 di dh px di To use higher order differential eguations you must specify each rate of change on a separate line For example yx df dx E 4 0 a di n Modellus solves differential equations using Runge Kutta fourth order method with a default step of 0 1 which results in exact solutions for many equations If necessary for example with high frequency or stiff systems reduce the time step in the Options button of the Control window 64 Modellus Manual version 2 5 2002 ADVANCED The following is a valid iterative model Slas 1 To insert the last operator click or use the key After entering the iterative model you need to assign values to parameters and to the initial values of variables that iterate In this case you need to assign an initial value for n in the Initial Conditions window It is convenient to check the box Iterative Model in the Options button of the Control Window in particular if you want to use t as an iterated variable on the model An iterative model is computed sequentially The following is an iterative model that illustrates Euler method for an oscillator Control FI EE pE e Ee meme J Bal Ei 100000000 O VX Jast x 0 5x x x at X FlastX last X df Initial Conditions
56. steps in the text box Tracking is associated with the time step specified in the Control Options dialog box Each image frame in the track is equivalent to a time step For example if the time step is set at 0 1 and you specify tracking at every 10 steps then Modellus will show one image per second Geometric Object Lx C Segments Polygon Circle C Line HORIZONTAL scales Origin Var Axes bd Var Axes H No of points Name Attributes M Name M Value M Points M Axis Filled Trajectory Tracking Track every steps Cancel Delete Colour mau Thickness 1 Fl VERTICAL 86 Modellus Manual version 2 5 2002 PLE OF THE PLE FILES 87 Modellus Manual version 2 5 2002 blank page 88 Modellus Manual version 2 5 2002 SAMPLE FILES File c Program files modellus 2 5 tutorial 05 making a model from data mdl x Modellus C Modellus 2 5 tutorial 05 making a model from data mdl File Edit Case Window Help Control E xi HEI 5 X 1 Position m This car has a vector v on it Create a vector place it over the image and link it to the image See the properties of this vector and of the image with the right button pe tool to measure slopes es to have a direct t of the slope 40867 scale p 0 01071 he scales of th As on scale v 0 01093 scale t 0 02167 Time s 7 scale t 323
57. t 18 46 Double click to set origin Click and drag to zoom x0 A xsin w xt size 7 30 if 1 gt delay then x 4 xsin w x delay if 1 gt 2x delay then x2 4 xsin w x t 2x delay if 1 gt 3x delay then x3 4 xsin w x 1 3 delay if 1 gt 4x delay then x4 4 xsin w x 1 4x delay if 1 gt 5x delay then x5 4 xsin w x 1 5x delay if 1 gt 6x delay then x6 4 xsin w x 1 6x delay if 1 gt 7x delay then x7 4 xsin w x 1 7x delay if 1 gt 8x delay then x8 4 xsin w x 1 8x delay and so on if 1 79x delay then x9 4 xsin w x 1 9 x delay 91 Modellus Manual version 2 5 2002 SAMPLE FILES Doppler shift File c Program files modellus 2 5 dopler mdl Modellus C Modellus 2 5 dopler mdl Ele Edit Case Window Help 3 Animation 1 ON Relativistic effect OFF lax 10 00 Advancing Physics Simon Carson 9 9 originx lengthy origin 2 1 if switch 0 then lambda wavelength x 142 if switch 1 then lambda wavelength cl lambda x v if 1 lt lambda then 71 7 c1 if gt lambda then 7 c1 t lambda c2 2 lambda x v if 2x lambda then 72 c2 if 1 gt 2x lambda then 2 c2 1 2x lambda c3 3 x lambda x v if 3x lambda then 73 c3 if 1 gt 3x lambda then 73 c3 1 3 x lambda c4 74x lambda x v if 1 lt 4x lambda then 74 c4 if 1 gt 4x lambda
58. tes i i Name Iv Axis Iv Axis M Pencil M Pencil Iv Projection Lines Iv Projection Lines Scales C Points Scales C Points 1 Pixel fi 1Pe E___ Line aPxa pi _ 1Pxe P_ _ eine Colour MM gt Colour MI gt Thickness Thickness Cancel Delete Cancel Delete 55 Modellus Manual version 2 5 2002 INTERMEDIATE 20 To join two objects just place one object on top of the other For example to attach a vector named velocity to a ball named greenball drag a Vector on top of the ball When you do this you ll see the picture of a knot Click the left ja ono mouse button In the prompt box that appears click Yes The vector and ball are now attached You can move them around the window while they are joined You can attach the following objects to one another e particle ball rectangle referential e vector e digital meter o text Vector linked to greenball HORIZONTAL VERTICAL Name e geometric object s ion const Attributes se M Name Note When joining objects it is useful to give v p v AXIS them meaningful names Named objects are v Arrow N Tracki easier to edit and keep track of SA Scales Track every steps 1 Pixel 1 Pixel r Origin C Components To release the vector from the ball in the Var Var Resultant preceding example right click the joined Colour objects Thickness 3 gt Cancel Delete
59. then 74 c4 1 4x lambda c3 75x lambda x v if 1 lt 5x lambda then 75 c3 if 1 gt 5x lambda then 75 c5 1t 5x lambda Modellus Manual version 2 5 2002 SAMPLE FILES File c Program files modellus 2 5 free fall e poema para Galileu mdl y 0 783984 Ant nio Gede o Eu queria agradecer te G a intelig ncia das coisas B x u e quantos milh es de hor a quem tu esclareceste ia jurar que disparate G e jurava de p s juntos e sem a menor hesita o 83 Modellus C Modellus 2 5 free fall e poema para Galileu mdl la x File Edit Case Window Help Mode amp A imation 1 _ Control x 3 lu im mE Lebel Le ax E Ed 0 80 3 Co m T ni 2 S t 0 399996 Pesas options S N 98 m D 2 y Ea XI W CD Ro W D 0 80 10 80 E x W D 98 e O 10_80 0 404061 1 tlimage sc 0 002326 30 to O tlimage 0 033333 w D POEMA PARA GALILEU N W Q tlimage 30 93 Modellus Manual version 2 5 2002 SAMPLE FILES Functions File c Program files modellus 2 5 common functions in physics mdl ts Animation 1 Se Era v exponential 7420 66 a mear 30 00 Q0 DE B uj n 11 oscillation 4 08 inverse 1 00 ETE S Ap mirit decay 0 34 parabola 1030 00 ke decay A0 xe a if t gt 0 then inverse i if 0 then inverse os
60. tor or bar 4 Set the maximum to 10 Cancel Delete 5 Click OK and run the model 28 Modellus Manual version 2 5 2002 Animation 1 ae O qu in EI E Click on the Graph button 2 Click anywhere in the Animation Ef S TT m window nj M Name 3 Select the 7 Value variable t to be M Axis M Pencil M Projection Lines displayed in the horizontal axis and the variable x to be displayed in the vertical axis Colour BI Thickness C Points Line 4 Change Colour Cancel Delete and Thickness E Rama Ww a 5 Click OK and run Plotter a the model HORIZONTAL VERTI 6 Click with the RIGHT button on the origin of the graph or on the My i I Animation 1 pencil Scales Zi EEE 1 Pixel 0 2 1Pixe 7 Change the horizontal scale to 0 2 and run the model again RA A AKAKAAAAMAMMAANMN Ni PAE AEP I A IPP R R OO EIEBETSIPISTSTRE ff 29 Modellus Manual version 2 5 2002 digital meter in the ation window E Animation 1 O p n D n El 1 Click on the Digital Meter button BRE RRO s e 5 2 Click anywhere in the Animation window Digital Meter Heter Digital Meter 3 Select the Ci HORIZONTAL VERTICAL variable x to ve W n be E M Name Colour Mm 4 Change Font to K Cancel Delete Release Size 16 5 Cl
61. usly protected model e Open the file that contains the model with the password you want to remove e Choose Password from the File menu The Password Removal dialog box appears Password removal E3 Password OK Cancel e Type the password that was assigned to the model Click OK The model is no longer password protected 44 INTERMEDIATE 9 Modellus Manual version 2 5 2002 m m UT The following buttons are common to most windows Hide the window Useful to customize environments When you want to see the window again open the Window menu and choose the window you want to view The window reappears on your screen Whenever you open a new Graph Animation or Table window all hidden windows reappear Copy the window content to the clipboard In the Model Graph and Animation windows the button copies the content as an image In the Table window it copies the content as a table of data And in the Notes and Model windows selected text it copies the content as text Text can also be pasted in Model and Notes windows Print the window content Copy and Paste to a word processor may yield better results and comments can easily be added in the word processor file The hide button doesn t close the window it only hides it To close a window use the close button x on the top right of the window Model Notes Initial Conditions and Control windows can t be closed All Modellus menus are
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