Calculus III: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=158
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 19 Nov 2017 08:46:43 GMTSun, 19 Nov 2017 08:46:43 GMTNew applications in the Calculus III categoryhttp://www.mapleprimes.com/images/mapleapps.gifCalculus III: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=158
Multiple integrals over sets defined by inequalities
https://www.maplesoft.com/applications/view.aspx?SID=154350&ref=Feed
The aim of this worksheet is to present a method for computing multiple integrals of a function in n variables over a set defined by inequalities.<img src="/view.aspx?si=154350/nint.png" alt="Multiple integrals over sets defined by inequalities" align="left"/>The aim of this worksheet is to present a method for computing multiple integrals of a function in n variables over a set defined by inequalities.154350Wed, 25 Oct 2017 04:00:00 ZProf. Valeriu AnisiuProf. Valeriu AnisiuMoment of a force using vectors
https://www.maplesoft.com/applications/view.aspx?SID=154345&ref=Feed
The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.<img src="/view.aspx?si=154345/moment of force.PNG" alt="Moment of a force using vectors" align="left"/>The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.154345Tue, 26 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloVector space with projections and forces
https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=Feed
With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.<img src="/view.aspx?si=154294/vectors.PNG" alt="Vector space with projections and forces" align="left"/>With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.154294Mon, 11 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloDisplacement and distance traveled with vectors
https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=Feed
In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.<img src="/view.aspx?si=154293/desplvp.png" alt="Displacement and distance traveled with vectors" align="left"/>In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.154293Mon, 28 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of Position Vector
https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=Feed
This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.<img src="/view.aspx?si=154290/bnrvp.png" alt="Plot of Position Vector" align="left"/>This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.154290Thu, 10 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloKinematics using syntax
https://www.maplesoft.com/applications/view.aspx?SID=154271&ref=Feed
In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.<img src="/view.aspx?si=154271/kinematicssint.png" alt="Kinematics using syntax" align="left"/>In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.154271Wed, 14 Jun 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMathematics for Chemistry
https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=Feed
This interactive electronic textbook in the form of Maple worksheets comprises two parts.
<BR><BR>
Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
<BR><BR>
Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
<BR><BR>
Other chapters are in preparation and will be released in due course.<img src="/view.aspx?si=154267/molecule.PNG" alt="Mathematics for Chemistry" align="left"/>This interactive electronic textbook in the form of Maple worksheets comprises two parts.
<BR><BR>
Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
<BR><BR>
Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
<BR><BR>
Other chapters are in preparation and will be released in due course.154267Tue, 30 May 2017 04:00:00 ZProf. John OgilvieProf. John OgilvieVector Force
https://www.maplesoft.com/applications/view.aspx?SID=154245&ref=Feed
This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. This is an easy-to-use interactive application. In Spanish.<img src="/view.aspx?si=154245/vecfza.png" alt="Vector Force" align="left"/>This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. This is an easy-to-use interactive application. In Spanish.154245Tue, 09 May 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloClassroom Tips and Techniques: Roles for the Laplace Transform's Shifting Laws
https://www.maplesoft.com/applications/view.aspx?SID=1723&ref=Feed
The shifting laws for the Laplace transform are examined, and the argument is made that the transform of f(t) Heaviside(t - a) should be done with the third shifting law, reserving the second shifting law strictly for inverting functions of the form e^(-a s) F(s). It is needlessly complicated to apply the second shifting law to functions of the form f(t) Heaviside(t - a)<img src="/view.aspx?si=1723/laplace.PNG" alt="Classroom Tips and Techniques: Roles for the Laplace Transform's Shifting Laws" align="left"/>The shifting laws for the Laplace transform are examined, and the argument is made that the transform of f(t) Heaviside(t - a) should be done with the third shifting law, reserving the second shifting law strictly for inverting functions of the form e^(-a s) F(s). It is needlessly complicated to apply the second shifting law to functions of the form f(t) Heaviside(t - a)1723Tue, 25 Apr 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezInterpretación geométrica del proceso de solución de una ecuación trigonométrica
https://www.maplesoft.com/applications/view.aspx?SID=154110&ref=Feed
Esta aplicación tiene como objetivo ayudar al estudiante a comprender el significado geométrico de resolver la ecuación trigonométrica sen(theta) = c en un intervalo de longitud 2Pi.
La barra deslizante de la aplicación permite variar el valor de c, mientras que los gráficos ayudan al estudiante a visualizar y comprender el proceso de búsqueda de soluciones de la ecuación trigonométrica de interés.<img src="/view.aspx?si=154110/232a3a3435a381a76ee84170be3fcee2.gif" alt="Interpretación geométrica del proceso de solución de una ecuación trigonométrica" align="left"/>Esta aplicación tiene como objetivo ayudar al estudiante a comprender el significado geométrico de resolver la ecuación trigonométrica sen(theta) = c en un intervalo de longitud 2Pi.
La barra deslizante de la aplicación permite variar el valor de c, mientras que los gráficos ayudan al estudiante a visualizar y comprender el proceso de búsqueda de soluciones de la ecuación trigonométrica de interés.154110Tue, 24 May 2016 04:00:00 ZRanferi GutierrezRanferi GutierrezThe Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae
https://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 BaroudyGuia de estudio para integrales dobles
https://www.maplesoft.com/applications/view.aspx?SID=153595&ref=Feed
<p>Esta guía de estudio tiene como objetivo aprovechar las capacidades de Maple para generar gráficas interactivas y lograr con ellas que el estudiante comprenda el problema geométrico que da origen a la integral doble, la interpretación geométrica de una integral doble cuando el integrando es positivo, y la interpretación geométrica del cálculo de integrales iteradas en una integral doble.</p><img src="/view.aspx?si=153595/Preview_figure.png" alt="Guia de estudio para integrales dobles" align="left"/><p>Esta guía de estudio tiene como objetivo aprovechar las capacidades de Maple para generar gráficas interactivas y lograr con ellas que el estudiante comprenda el problema geométrico que da origen a la integral doble, la interpretación geométrica de una integral doble cuando el integrando es positivo, y la interpretación geométrica del cálculo de integrales iteradas en una integral doble.</p>153595Tue, 03 Jun 2014 04:00:00 ZDr. Ranferi GutierrezDr. Ranferi GutierrezGuia electronica de estudio sobre Multiplicadores de Lagrange
https://www.maplesoft.com/applications/view.aspx?SID=153587&ref=Feed
<p>El objetivo principal de la presente guia electronica de estudio es que el estudiante adquiera una comprension geometrica de lo que significa buscar valores extremos de una funcion de varias variables, la cual esta sujeta a una restriccion. El objetivo principal de esta guia se logra aprovechando las capacidades de Maple para generar graficos en 3D y manipularlos a traves del uso de componentes.</p><img src="/view.aspx?si=153587/multiplicadores.png" alt="Guia electronica de estudio sobre Multiplicadores de Lagrange" align="left"/><p>El objetivo principal de la presente guia electronica de estudio es que el estudiante adquiera una comprension geometrica de lo que significa buscar valores extremos de una funcion de varias variables, la cual esta sujeta a una restriccion. El objetivo principal de esta guia se logra aprovechando las capacidades de Maple para generar graficos en 3D y manipularlos a traves del uso de componentes.</p>153587Tue, 20 May 2014 04:00:00 ZDr. Ranferi GutierrezDr. Ranferi GutierrezClassroom Tips and Techniques: Drawing a Normal and Tangent Plane on a Surface
https://www.maplesoft.com/applications/view.aspx?SID=150722&ref=Feed
Four different techniques are given for obtaining a graph showing a surface with a normal and tangent plane attached. The work is a response to <a href="http://www.mapleprimes.com/questions/147681-A-Problem-About-Plot-The-Part-Of-The-Surface">a MaplePrimes question asked on May 25, 2013</a>.<img src="/view.aspx?si=150722/thumb.jpg" alt="Classroom Tips and Techniques: Drawing a Normal and Tangent Plane on a Surface" align="left"/>Four different techniques are given for obtaining a graph showing a surface with a normal and tangent plane attached. The work is a response to <a href="http://www.mapleprimes.com/questions/147681-A-Problem-About-Plot-The-Part-Of-The-Surface">a MaplePrimes question asked on May 25, 2013</a>.150722Tue, 20 Aug 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: New Tools for Lines and Planes
https://www.maplesoft.com/applications/view.aspx?SID=144642&ref=Feed
The fifteen new "Lines and Planes" commands in the Student MultivariateCalculus package are detailed, and then illustrated via a collection of examples from a typical calculus course. These new commands can also be implemented through the Context Menu system, as shown by parallel solutions in the set of examples.<img src="/view.aspx?si=144642/thumb.jpg" alt="Classroom Tips and Techniques: New Tools for Lines and Planes" align="left"/>The fifteen new "Lines and Planes" commands in the Student MultivariateCalculus package are detailed, and then illustrated via a collection of examples from a typical calculus course. These new commands can also be implemented through the Context Menu system, as shown by parallel solutions in the set of examples.144642Thu, 14 Mar 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Animated Trace of a Curve Drawn by Radius Vector
https://www.maplesoft.com/applications/view.aspx?SID=143371&ref=Feed
A plane curve <strong>R</strong>(<em>t</em>) = <em>x</em>(<em>t</em>) <strong>i</strong> + <em>y</em>(<em>t</em>) <strong>j</strong> is traced by a "moving" radius vector <strong>R</strong>(<em>t</em>). Code for this animation is explored in this article.<img src="/view.aspx?si=143371/thumb.jpg" alt="Classroom Tips and Techniques: Animated Trace of a Curve Drawn by Radius Vector" align="left"/>A plane curve <strong>R</strong>(<em>t</em>) = <em>x</em>(<em>t</em>) <strong>i</strong> + <em>y</em>(<em>t</em>) <strong>j</strong> is traced by a "moving" radius vector <strong>R</strong>(<em>t</em>). Code for this animation is explored in this article.143371Mon, 11 Feb 2013 05:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Least-Squares Fits
https://www.maplesoft.com/applications/view.aspx?SID=140942&ref=Feed
<p><span id="ctl00_mainContent__documentViewer" ><span ><span class="body summary">The least-squares fitting of functions to data can be done in Maple with eleven different commands from four different packages. The <em>CurveFitting</em> and LinearAlgebra packages each have a LeastSquares command; the Optimization package has the LSSolve and NLPSolve commands; and the Statistics package has the seven commands Fit, LinearFit, PolynomialFit, ExponentialFit, LogarithmicFit, PowerFit, and NonlinearFit, which can return some measure of regression analysis.</span></span></span></p><img src="/view.aspx?si=140942/image.jpg" alt="Classroom Tips and Techniques: Least-Squares Fits" align="left"/><p><span id="ctl00_mainContent__documentViewer" ><span ><span class="body summary">The least-squares fitting of functions to data can be done in Maple with eleven different commands from four different packages. The <em>CurveFitting</em> and LinearAlgebra packages each have a LeastSquares command; the Optimization package has the LSSolve and NLPSolve commands; and the Statistics package has the seven commands Fit, LinearFit, PolynomialFit, ExponentialFit, LogarithmicFit, PowerFit, and NonlinearFit, which can return some measure of regression analysis.</span></span></span></p>140942Wed, 28 Nov 2012 05:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: An Inequality-Constrained Optimization Problem
https://www.maplesoft.com/applications/view.aspx?SID=135904&ref=Feed
<p>This article shows how to work both analytically and numerically to find the global maximum of</p>
<p><em>w</em> = ƒ(<em>x, y, z</em>) ≡ <em>x</em><sup>2</sup>(1 + <em>x</em>) + <em>y</em><sup>2</sup>(1 + <em>y</em>) + z<sup>2</sup>(1 + <em>z</em>)</p>
<p>in that part of the first octant on, or below, the plane <em>x</em> + <em>y</em> + <em>z</em> = 6.</p><img src="/view.aspx?si=135904/thumb.jpg" alt="Classroom Tips and Techniques: An Inequality-Constrained Optimization Problem" align="left"/><p>This article shows how to work both analytically and numerically to find the global maximum of</p>
<p><em>w</em> = ƒ(<em>x, y, z</em>) ≡ <em>x</em><sup>2</sup>(1 + <em>x</em>) + <em>y</em><sup>2</sup>(1 + <em>y</em>) + z<sup>2</sup>(1 + <em>z</em>)</p>
<p>in that part of the first octant on, or below, the plane <em>x</em> + <em>y</em> + <em>z</em> = 6.</p>135904Mon, 16 Jul 2012 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Custom and Task Palettes
https://www.maplesoft.com/applications/view.aspx?SID=132914&ref=Feed
New in Maple 16, the Custom palette is a palette added to Maple by the user. It is populated with task templates that are already in the Task Browser Table of Contents. A separate Tasks palette can be populated with task templates created by the "Create Task" option in the Context Menu for any selection in a worksheet. This article sheds light on these new functionalities, and gives an example of a Custom palette developed to capture part of the geom3d package in task templates.<img src="/view.aspx?si=132914/thumb.jpg" alt="Classroom Tips and Techniques: Custom and Task Palettes" align="left"/>New in Maple 16, the Custom palette is a palette added to Maple by the user. It is populated with task templates that are already in the Task Browser Table of Contents. A separate Tasks palette can be populated with task templates created by the "Create Task" option in the Context Menu for any selection in a worksheet. This article sheds light on these new functionalities, and gives an example of a Custom palette developed to capture part of the geom3d package in task templates.132914Thu, 12 Apr 2012 04:00:00 ZDr. Robert LopezDr. Robert LopezSpherical Pendulum with Animation
https://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