General: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=162
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 07 Feb 2016 05:53:13 GMTSun, 07 Feb 2016 05:53:13 GMTNew applications in the General categoryhttp://www.mapleprimes.com/images/mapleapps.gifGeneral: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=162
Holiday Greetings and Tupper’s Self-Referential Formula
http://www.maplesoft.com/applications/view.aspx?SID=153935&ref=Feed
Want to send a Holiday greeting to a fellow Maple user? Then send them this worksheet - it's a seasonal spin on the classic Tupper’s Self-Referential Formula.<img src="/view.aspx?si=153935/teaserimage.png" alt="Holiday Greetings and Tupper’s Self-Referential Formula" align="left"/>Want to send a Holiday greeting to a fellow Maple user? Then send them this worksheet - it's a seasonal spin on the classic Tupper’s Self-Referential Formula.153935Fri, 11 Dec 2015 05:00:00 ZSamir KhanSamir KhanEscapeTime Fractals
http://www.maplesoft.com/applications/view.aspx?SID=153882&ref=Feed
<P>
The <A HREF="/support/help/Maple/view.aspx?path=Fractals/EscapeTime">Fractals</A> package in Maple makes it easier to create and explore popular fractals, including the Mandelbrot, Julia, Newton, and other time-iterative fractals. The Fractals package can quickly apply various escape time iterative maps over rectangular regions in the complex plane, the results of which consist of images that approximate well-known fractal sets. In the following application, you can explore escape time fractals by manipulating parameters pertaining to the generation of Mandelbrot, Julia, Newton and Burning Ship fractals.</P>
<P>
<B>Also:</B> You can <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=5690839489576960">interact with this application</A> in the MapleCloud!</P><img src="/view.aspx?si=153882/escapetimefractal.png" alt="EscapeTime Fractals" align="left"/><P>
The <A HREF="/support/help/Maple/view.aspx?path=Fractals/EscapeTime">Fractals</A> package in Maple makes it easier to create and explore popular fractals, including the Mandelbrot, Julia, Newton, and other time-iterative fractals. The Fractals package can quickly apply various escape time iterative maps over rectangular regions in the complex plane, the results of which consist of images that approximate well-known fractal sets. In the following application, you can explore escape time fractals by manipulating parameters pertaining to the generation of Mandelbrot, Julia, Newton and Burning Ship fractals.</P>
<P>
<B>Also:</B> You can <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=5690839489576960">interact with this application</A> in the MapleCloud!</P>153882Fri, 25 Sep 2015 04:00:00 ZMaplesoftMaplesoftMaplets de sudoku GSudoku5M et SudokuE8f-L
http://www.maplesoft.com/applications/view.aspx?SID=153753&ref=Feed
<p>Les 2 interfaces pour le sudoku généralisé à régions n*m</p>
<p>(on peut insérer e et r dans rectangle rouge de la maplet GSudoku5L pour effacer et avoir la réponse)</p>
<p>(on peut utiliser ds4windows pour jouer avec une manette Dualshock 4 à GSudoku5M en utilisant "Alt+key"</p><img src="/view.aspx?si=153753/CaptGSudoku5h.JPG" alt="Maplets de sudoku GSudoku5M et SudokuE8f-L" align="left"/><p>Les 2 interfaces pour le sudoku généralisé à régions n*m</p>
<p>(on peut insérer e et r dans rectangle rouge de la maplet GSudoku5L pour effacer et avoir la réponse)</p>
<p>(on peut utiliser ds4windows pour jouer avec une manette Dualshock 4 à GSudoku5M en utilisant "Alt+key"</p>153753Fri, 18 Sep 2015 04:00:00 Zxavier cormierxavier cormierKnight's Tour
http://www.maplesoft.com/applications/view.aspx?SID=153842&ref=Feed
A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once.
This application presents the implementation of this task in Maple.<img src="/view.aspx?si=153842/26f19bd457ac566083dec1b86db8b91b.gif" alt="Knight's Tour" align="left"/>A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once.
This application presents the implementation of this task in Maple.153842Thu, 13 Aug 2015 04:00:00 ZDr. Yury ZavarovskyDr. Yury ZavarovskyRepresentation Triangles for Three Candidate Elections
http://www.maplesoft.com/applications/view.aspx?SID=135757&ref=Feed
<p>This application takes ranking data from a three person election and creates representation triangles that depict the results of the election both numerically and geometrically for a number of different voting systems. The numerical profile makes it straightforward to calculate the results of the election under a number of different systems while the geometric profile displays the procedure line and the approval voting region and specifically the plurality, anti-plurality and Borda count results. </p>
<p>This is an improvement over the first author's earlier, similar application. The geometric profile is rendered as a two-dimensional object and additional election results are made explicit.</p><img src="/view.aspx?si=135757/135757_thumb.jpg" alt="Representation Triangles for Three Candidate Elections" align="left"/><p>This application takes ranking data from a three person election and creates representation triangles that depict the results of the election both numerically and geometrically for a number of different voting systems. The numerical profile makes it straightforward to calculate the results of the election under a number of different systems while the geometric profile displays the procedure line and the approval voting region and specifically the plurality, anti-plurality and Borda count results. </p>
<p>This is an improvement over the first author's earlier, similar application. The geometric profile is rendered as a two-dimensional object and additional election results are made explicit.</p>135757Thu, 11 Jun 2015 04:00:00 ZDr. Joseph KolacinskiDr. Joseph KolacinskiSudoku tactile généralisé (version finale)
http://www.maplesoft.com/applications/view.aspx?SID=124424&ref=Feed
<p>Mes 3 maplets de sudoku (à régions n*m) en version finale.</p>
<p>(SudokuE8f-L avec radiobutton,GSudoku3 avec popupmenu et GSudoku4 avec popupmenu et croix directionnelle).</p><img src="/view.aspx?si=124424/capsud.PNG" alt="Sudoku tactile généralisé (version finale)" align="left"/><p>Mes 3 maplets de sudoku (à régions n*m) en version finale.</p>
<p>(SudokuE8f-L avec radiobutton,GSudoku3 avec popupmenu et GSudoku4 avec popupmenu et croix directionnelle).</p>124424Mon, 19 Jan 2015 05:00:00 Zxavier cormierxavier cormierThe Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae
http://www.maplesoft.com/applications/view.aspx?SID=153706&ref=Feed
<p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p><img src="/applications/images/app_image_blank_lg.jpg" alt="The Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae" align="left"/><p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p>153706Mon, 17 Nov 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyHollywood Math 2
http://www.maplesoft.com/applications/view.aspx?SID=153681&ref=Feed
<p>Over the years, Hollywood has entertained us with many mathematical moments in film and television, often in unexpected places. In this application, you’ll find several examples of Hollywood Math, including Fermat’s Last Theorem and <em>The Simpsons</em>, the Monty Hall problem in <em>21</em>, and a discussion of just how long that runway actually was in <em>The Fast and the Furious</em>. These examples are also presented in <a href="/webinars/recorded/featured.aspx?id=782">Hollywood Math 2: The Recorded Webinar</a>.</p>
<p>For even more examples, see <a href="/applications/view.aspx?SID=6611">Hollywood Math: The Original Episode</a>.</p><img src="/view.aspx?si=153681/HollywoodMath2.jpg" alt="Hollywood Math 2" align="left"/><p>Over the years, Hollywood has entertained us with many mathematical moments in film and television, often in unexpected places. In this application, you’ll find several examples of Hollywood Math, including Fermat’s Last Theorem and <em>The Simpsons</em>, the Monty Hall problem in <em>21</em>, and a discussion of just how long that runway actually was in <em>The Fast and the Furious</em>. These examples are also presented in <a href="/webinars/recorded/featured.aspx?id=782">Hollywood Math 2: The Recorded Webinar</a>.</p>
<p>For even more examples, see <a href="/applications/view.aspx?SID=6611">Hollywood Math: The Original Episode</a>.</p>153681Tue, 23 Sep 2014 04:00:00 ZMaplesoftMaplesoftDescartes & Mme La Marquise du Chatelet And The Elastic Collision of Two Bodies
http://www.maplesoft.com/applications/view.aspx?SID=153515&ref=Feed
<p><strong><em> ABSTRACT<br /> <br /> The Marquise</em></strong> <strong><em>du Chatelet in her book " Les Institutions Physiques" published in 1740, stated on page 36, that Descartes, when formulating his laws of motion in an elastic collision of two bodies B & C (B being more massive than C) <span >having the same speed v</span>, said that t<span >he smaller one C will reverse its course </span>while <span >the more massive body B will continue its course in the same direction as before</span> and <span >both will have again the same speed v.<br /> <br /> </span>Mme du Chatelet, basing her judgment on theoretical considerations using <span >the principle of continuity</span> , declared that Descartes was <span >wrong</span> in his statement. For Mme du Chatelet the larger mass B should reverse its course and move in the opposite direction. She mentioned nothing about both bodies B & C as <span >having the same velocity after collision as Descartes did</span>.<br /> <br /> At the time of Descartes, some 300 years ago, the concept of kinetic energy & momentum as we know today was not yet well defined, let alone considered in any physical problem.<br /> <br /> Actually both Descartes & Mme du Chatelet may have been right in some special cases but not in general as the discussion that follows will show.</em></strong></p><img src="/view.aspx?si=153515/Elastic_Collision_image1.jpg" alt="Descartes & Mme La Marquise du Chatelet And The Elastic Collision of Two Bodies" align="left"/><p><strong><em> ABSTRACT<br /> <br /> The Marquise</em></strong> <strong><em>du Chatelet in her book " Les Institutions Physiques" published in 1740, stated on page 36, that Descartes, when formulating his laws of motion in an elastic collision of two bodies B & C (B being more massive than C) <span >having the same speed v</span>, said that t<span >he smaller one C will reverse its course </span>while <span >the more massive body B will continue its course in the same direction as before</span> and <span >both will have again the same speed v.<br /> <br /> </span>Mme du Chatelet, basing her judgment on theoretical considerations using <span >the principle of continuity</span> , declared that Descartes was <span >wrong</span> in his statement. For Mme du Chatelet the larger mass B should reverse its course and move in the opposite direction. She mentioned nothing about both bodies B & C as <span >having the same velocity after collision as Descartes did</span>.<br /> <br /> At the time of Descartes, some 300 years ago, the concept of kinetic energy & momentum as we know today was not yet well defined, let alone considered in any physical problem.<br /> <br /> Actually both Descartes & Mme du Chatelet may have been right in some special cases but not in general as the discussion that follows will show.</em></strong></p>153515Fri, 07 Mar 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyWavelet analysis of the blood pressure and pulse frequency measurements with Maple
http://www.maplesoft.com/applications/view.aspx?SID=149420&ref=Feed
<p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p><img src="/view.aspx?si=149420/4b9024ee653d2c7be8febb717b1df52a.gif" alt="Wavelet analysis of the blood pressure and pulse frequency measurements with Maple" align="left"/><p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p>149420Sun, 14 Jul 2013 04:00:00 ZIrina A. DanishewskaIrina A. DanishewskaPerimeter, area and visualization of a plane figure
http://www.maplesoft.com/applications/view.aspx?SID=146470&ref=Feed
<p>The work contains three procedures that allow symbolically to calculate the perimeter and area of any plane figure bounded by <span>non-selfintersecting piecewise smooth curve</span>, and to portray this figure together with its boundary in a suitable design.</p><img src="/view.aspx?si=146470/planefigure_thumb.png" alt="Perimeter, area and visualization of a plane figure" align="left"/><p>The work contains three procedures that allow symbolically to calculate the perimeter and area of any plane figure bounded by <span>non-selfintersecting piecewise smooth curve</span>, and to portray this figure together with its boundary in a suitable design.</p>146470Tue, 30 Apr 2013 04:00:00 ZDr. Yury ZavarovskyDr. Yury ZavarovskyCar Loan Calculator
http://www.maplesoft.com/applications/view.aspx?SID=145174&ref=Feed
<p>This loan calculator facilitates the life of a borrower. By entering the <strong>purchase price</strong>, the <strong>down payment</strong>, the <strong>number of years</strong> it takes to repay the loan, the <strong>payment frequency</strong>, the <strong>annual interest rate</strong>, and clicking on the "<strong>calculate</strong>" buttom, the calculator will give you the <strong>amount of payment</strong> for each payment period.</p>
<p> </p>
<p>Want to make a loan? Try it out and see how things change with respect to each element.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Car Loan Calculator" align="left"/><p>This loan calculator facilitates the life of a borrower. By entering the <strong>purchase price</strong>, the <strong>down payment</strong>, the <strong>number of years</strong> it takes to repay the loan, the <strong>payment frequency</strong>, the <strong>annual interest rate</strong>, and clicking on the "<strong>calculate</strong>" buttom, the calculator will give you the <strong>amount of payment</strong> for each payment period.</p>
<p> </p>
<p>Want to make a loan? Try it out and see how things change with respect to each element.</p>145174Wed, 27 Mar 2013 04:00:00 ZZinan WangZinan WangCalculation of the Average Duration of an Illness and Computation of the Reproduction Number in the SIR Model
http://www.maplesoft.com/applications/view.aspx?SID=142794&ref=Feed
<p>I prepared this Maple worksheet as part of a presentation to Professor Mubayi's lab group at Northeastern Illinois University. Every member of the research group explores a different aspect of how mathematics is used to study public health. During this presentation, I explore two different SIR models.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Calculation of the Average Duration of an Illness and Computation of the Reproduction Number in the SIR Model" align="left"/><p>I prepared this Maple worksheet as part of a presentation to Professor Mubayi's lab group at Northeastern Illinois University. Every member of the research group explores a different aspect of how mathematics is used to study public health. During this presentation, I explore two different SIR models.</p>142794Tue, 29 Jan 2013 05:00:00 ZDouglas LewitDouglas LewitMortgages
http://www.maplesoft.com/applications/view.aspx?SID=142213&ref=Feed
<p>Consider the problem of borrowing $250,000 to buy a house. You borrow the money at a fixed interest rate of 4.8% compounded monthly. The term of the mortgage is for 20 years. However, you decide against making minimum payments. Instead you decide to pay an additional $200 every month. How long will it take you to pay off the loan and how much have you saved on interest by paying off the loan early?</p><img src="/view.aspx?si=142213/b8fc2d4d03908eeda63c803f8bbd81c1.gif" alt="Mortgages" align="left"/><p>Consider the problem of borrowing $250,000 to buy a house. You borrow the money at a fixed interest rate of 4.8% compounded monthly. The term of the mortgage is for 20 years. However, you decide against making minimum payments. Instead you decide to pay an additional $200 every month. How long will it take you to pay off the loan and how much have you saved on interest by paying off the loan early?</p>142213Fri, 11 Jan 2013 05:00:00 ZDouglas LewitDouglas LewitGems 26-30 from the Red Book of Maple Magic
http://www.maplesoft.com/applications/view.aspx?SID=141091&ref=Feed
<p>In 2011, this column published five "Maple Magic" articles, each containing five "gems" gleaned from interactions with Maple and the Maplesoft programmers. Here are five more recent additions to the Red Book, every one of which contained something about Maple that was a surprise to me, experienced Maple user that I am.</p><img src="/view.aspx?si=141091/thumb.jpg" alt="Gems 26-30 from the Red Book of Maple Magic" align="left"/><p>In 2011, this column published five "Maple Magic" articles, each containing five "gems" gleaned from interactions with Maple and the Maplesoft programmers. Here are five more recent additions to the Red Book, every one of which contained something about Maple that was a surprise to me, experienced Maple user that I am.</p>141091Tue, 04 Dec 2012 05:00:00 ZDr. Robert LopezDr. Robert LopezSCRABBLE® Two Letter Words Quiz
http://www.maplesoft.com/applications/view.aspx?SID=139291&ref=Feed
<p>Players of SCRABBLE® and similar word games find it useful to know all the valid two-letter words. In the SCRABBLE® game, knowing these words allows you to find places where you can "hook" a word from your rack. This application tests your knowledge of the two-letter words. </p><img src="/view.aspx?si=139291/139291_thumb.jpg" alt="SCRABBLE® Two Letter Words Quiz" align="left"/><p>Players of SCRABBLE® and similar word games find it useful to know all the valid two-letter words. In the SCRABBLE® game, knowing these words allows you to find places where you can "hook" a word from your rack. This application tests your knowledge of the two-letter words. </p>139291Wed, 07 Nov 2012 05:00:00 ZDr. Paulina ChinDr. Paulina ChinSCRABBLE® Two-to-Make-Three Quiz
http://www.maplesoft.com/applications/view.aspx?SID=139293&ref=Feed
<p>Players of SCRABBLE® and similar word games find it useful to know all the valid three-letter words that can be formed from a valid two-letter word. For example, in the SCRABBLE® game, knowing these words allows you to find places where you can "hook" onto a word already on the board. This application below tests your knowledge of the hooks for two-letter words. </p><img src="/view.aspx?si=139293/139293_thumb.jpg" alt="SCRABBLE® Two-to-Make-Three Quiz" align="left"/><p>Players of SCRABBLE® and similar word games find it useful to know all the valid three-letter words that can be formed from a valid two-letter word. For example, in the SCRABBLE® game, knowing these words allows you to find places where you can "hook" onto a word already on the board. This application below tests your knowledge of the hooks for two-letter words. </p>139293Wed, 07 Nov 2012 05:00:00 ZDr. Paulina ChinDr. Paulina ChinMath Apps in Maple
http://www.maplesoft.com/applications/view.aspx?SID=132220&ref=Feed
Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains a sampling of some of the many Math Apps available in Maple: drawing the graph of a quadratic, epicycloids, monte carlo approximations of pi, and throwing coconuts.<img src="/view.aspx?si=132220/mathapps_thumb.png" alt="Math Apps in Maple" align="left"/>Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains a sampling of some of the many Math Apps available in Maple: drawing the graph of a quadratic, epicycloids, monte carlo approximations of pi, and throwing coconuts.132220Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftPolynomial System Solving in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132208&ref=Feed
Computing and manipulating the real solutions of a polynomial system is a requirement for many application areas, such as biological modeling, robotics, program verification, and control design, to name just a few. For example, an important problem in computational biology is to study the stability of the equilibria (or steady states) of biological systems. This question can often be reduced to solving a parametric system of polynomial equations and inequalities. In this application, these techniques are used to perform stability analysis of a parametric dynamical system and verify mathematical identities through branch cut analysis.<img src="/view.aspx?si=132208/thumb.jpg" alt="Polynomial System Solving in Maple 16" align="left"/>Computing and manipulating the real solutions of a polynomial system is a requirement for many application areas, such as biological modeling, robotics, program verification, and control design, to name just a few. For example, an important problem in computational biology is to study the stability of the equilibria (or steady states) of biological systems. This question can often be reduced to solving a parametric system of polynomial equations and inequalities. In this application, these techniques are used to perform stability analysis of a parametric dynamical system and verify mathematical identities through branch cut analysis.132208Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftSpherical Pendulum with Animation
http://www.maplesoft.com/applications/view.aspx?SID=132143&ref=Feed
<p>Some years ago I have written a Maple document ( already on Maple's online) on the subject of animating a simple pendulum for large angles of oscillation. This gave me the chance to test Maple command JacobiSN(time, k). I was very much pleased to see Maple do a wonderful job in getting these Jacobi's elliptic functions without a glitch.<br />Today I am back to these same functions for a similar purpose though much more sophisticated than the previous one.<br />The idea is:<br />1- to get the differential equations of motion for the Spherical Pendulum (SP),<br />2- to solve them,<br />3- to use Maple for finding the inverse of these Elliptic Integrals i.e. finding the displacement z as function of time,<br />4- to get a set of coordinates [x, y, z] for the positions of the bob at different times for plotting,<br />5- finally to work out the necessary steps for the purpose of animation.<br />It turns out that even with only 3 oscillations where each is defined with only 20 positions of the bob for a total of 60 points on the graph, the animation is so overwhelming that Maple reports:<br /> " the length of the output exceeds 1 million".<br />Not withstanding this warning, Maple did a perfect job by getting the animation to my satisfaction. <br />Note that with only 60 positions of the bob, the present article length is equal to 11.3 MB! To be able to upload it, I have to save it without running the last command related to the animation. Doing so I reduced it to a mere 570 KB.<br /><br />It was tiring to get through a jumble of formulas, calculations and programming so I wonder why I have to go through all this trouble to get this animation and yet one can get the same thing with much better animation from the internet. I think the reason is the challenge to be able to do things that others have done before and secondly the idea of creating something form nothing then to see it working as expected, gives (at least to me) a great deal of pleasure and satisfaction.<br />This is beside the fact that, to my knowledge, no such animation for (SP) has been published on Maple online with detailed calculations & programming as I did.<br /><br /></p><img src="/view.aspx?si=132143/433082\Spherical_Pendulum_p.jpg" alt="Spherical Pendulum with Animation" align="left"/><p>Some years ago I have written a Maple document ( already on Maple's online) on the subject of animating a simple pendulum for large angles of oscillation. This gave me the chance to test Maple command JacobiSN(time, k). I was very much pleased to see Maple do a wonderful job in getting these Jacobi's elliptic functions without a glitch.<br />Today I am back to these same functions for a similar purpose though much more sophisticated than the previous one.<br />The idea is:<br />1- to get the differential equations of motion for the Spherical Pendulum (SP),<br />2- to solve them,<br />3- to use Maple for finding the inverse of these Elliptic Integrals i.e. finding the displacement z as function of time,<br />4- to get a set of coordinates [x, y, z] for the positions of the bob at different times for plotting,<br />5- finally to work out the necessary steps for the purpose of animation.<br />It turns out that even with only 3 oscillations where each is defined with only 20 positions of the bob for a total of 60 points on the graph, the animation is so overwhelming that Maple reports:<br /> " the length of the output exceeds 1 million".<br />Not withstanding this warning, Maple did a perfect job by getting the animation to my satisfaction. <br />Note that with only 60 positions of the bob, the present article length is equal to 11.3 MB! To be able to upload it, I have to save it without running the last command related to the animation. Doing so I reduced it to a mere 570 KB.<br /><br />It was tiring to get through a jumble of formulas, calculations and programming so I wonder why I have to go through all this trouble to get this animation and yet one can get the same thing with much better animation from the internet. I think the reason is the challenge to be able to do things that others have done before and secondly the idea of creating something form nothing then to see it working as expected, gives (at least to me) a great deal of pleasure and satisfaction.<br />This is beside the fact that, to my knowledge, no such animation for (SP) has been published on Maple online with detailed calculations & programming as I did.<br /><br /></p>132143Mon, 26 Mar 2012 04:00:00 ZDr. Ahmed BaroudyDr. Ahmed Baroudy