Dynamical Systems: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=189
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 27 Oct 2016 22:38:08 GMTThu, 27 Oct 2016 22:38:08 GMTNew applications in the Dynamical Systems categoryhttp://www.mapleprimes.com/images/mapleapps.gifDynamical Systems: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=189
Exponential map fractal viewer
http://www.maplesoft.com/applications/view.aspx?SID=153953&ref=Feed
Static fractal viewer for the Julia sets of the exponential map lambda*exp(z), with variable lambda. Allows adjustable viewing window, zoom-in and display of periodic attractors up to period 5. Dynamic version can generate animated views, like the Knaster explosion of period 3 shown on the figure.<img src="/view.aspx?si=153953/3djulia.png" alt="Exponential map fractal viewer" align="left"/>Static fractal viewer for the Julia sets of the exponential map lambda*exp(z), with variable lambda. Allows adjustable viewing window, zoom-in and display of periodic attractors up to period 5. Dynamic version can generate animated views, like the Knaster explosion of period 3 shown on the figure.153953Tue, 19 Jan 2016 05:00:00 ZRobert Israel, Carl LoveRobert Israel, Carl LoveThe Classic SIR Model
http://www.maplesoft.com/applications/view.aspx?SID=153877&ref=Feed
<P>This interactive application explores the classical SIR model for the spread of disease, which assumes that a population can be divided into three distinct compartments - S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease.</P>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=4837052487041024">View and interact with this app in the MapleCloud!</A></P><img src="/view.aspx?si=153877/sir_classic.png" alt="The Classic SIR Model" align="left"/><P>This interactive application explores the classical SIR model for the spread of disease, which assumes that a population can be divided into three distinct compartments - S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease.</P>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=4837052487041024">View and interact with this app in the MapleCloud!</A></P>153877Wed, 16 Sep 2015 04:00:00 ZGünter EdenharterGünter EdenharterThe SIR model with births and deaths
http://www.maplesoft.com/applications/view.aspx?SID=153878&ref=Feed
<P>This interactive application explores a variation of the classic SIR model for the spread of disease. The classical SIR model assumes that a population can be divided into three distinct compartments: S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease. One extension to the classic SIR model is to add births and deaths to the model. Thus there is an inflow of new susceptibles and an outflow from all three compartments.</P>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6584880737550336">View and interact with this app in the MapleCloud!</A></P><img src="/view.aspx?si=153878/sir_births_deaths.png" alt="The SIR model with births and deaths" align="left"/><P>This interactive application explores a variation of the classic SIR model for the spread of disease. The classical SIR model assumes that a population can be divided into three distinct compartments: S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease. One extension to the classic SIR model is to add births and deaths to the model. Thus there is an inflow of new susceptibles and an outflow from all three compartments.</P>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6584880737550336">View and interact with this app in the MapleCloud!</A></P>153878Wed, 16 Sep 2015 04:00:00 ZGünter EdenharterGünter EdenharterThe SEIR model with births and deaths
http://www.maplesoft.com/applications/view.aspx?SID=153879&ref=Feed
<P>This interactive application explores the SEIR model for the spread of disease. The SEIR model is an extension of the classical SIR (Susceptibles, Infected, Recovered) model, where a fourth compartment is added that contains exposed persons which are infected but are not yet infectious. The SEIR (Susceptibles, Exposed, Infectious, Recovered) model as presented here covers also births and deaths.</P>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6407056173039616">View and interact with this app in the MapleCloud!</A></P><img src="/view.aspx?si=153879/seir.png" alt="The SEIR model with births and deaths" align="left"/><P>This interactive application explores the SEIR model for the spread of disease. The SEIR model is an extension of the classical SIR (Susceptibles, Infected, Recovered) model, where a fourth compartment is added that contains exposed persons which are infected but are not yet infectious. The SEIR (Susceptibles, Exposed, Infectious, Recovered) model as presented here covers also births and deaths.</P>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6407056173039616">View and interact with this app in the MapleCloud!</A></P>153879Wed, 16 Sep 2015 04:00:00 ZGünter EdenharterGünter EdenharterThe 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 BaroudyDescartes & 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="/applications/images/app_image_blank_lg.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 BaroudyDynamics of the Battlefield: The Lanchester Model
http://www.maplesoft.com/applications/view.aspx?SID=146801&ref=Feed
<p>Around the time of World War I, July 28, 1914 to November 11, 1918, many mathematicians and engineers, including Frederick W. Lanchester, became fascinated by the dynamics of the battlefield. Various mathematical models were proposed in an effort to explain--and to predict--how military forces interacted on the battlefield. During World War I these mathematical investigations were mainly academic, although during World War II the United States government actually applied these models to make important decisions about the Battle of Iwo Jima in which the American forces seized control of the Japanese island of Iwo Jima. Outnumbered and outgunned by the Americans, the Japanese were defeated even before the battle began although the American forces suffered many casualties and injuries.</p><img src="/view.aspx?si=146801/army2.JPG" alt="Dynamics of the Battlefield: The Lanchester Model" align="left"/><p>Around the time of World War I, July 28, 1914 to November 11, 1918, many mathematicians and engineers, including Frederick W. Lanchester, became fascinated by the dynamics of the battlefield. Various mathematical models were proposed in an effort to explain--and to predict--how military forces interacted on the battlefield. During World War I these mathematical investigations were mainly academic, although during World War II the United States government actually applied these models to make important decisions about the Battle of Iwo Jima in which the American forces seized control of the Japanese island of Iwo Jima. Outnumbered and outgunned by the Americans, the Japanese were defeated even before the battle began although the American forces suffered many casualties and injuries.</p>146801Mon, 06 May 2013 04:00:00 ZDouglas LewitDouglas LewitBifTools - Package for Bifurcation Analysis in Dynamical Systems
http://www.maplesoft.com/applications/view.aspx?SID=128951&ref=Feed
<p>BifTools is a package for symbolic and numeric bifurcation analysis of equilibrium points in dynamical systems. The package consists of five main procedures:</p>
<ul>
<li><strong>BifTools[calcOneZeroEigenvalueBifPoints]</strong> calculates the bifurcation points of an ODE system with a single zero eigenvalue of the Jacobian;</li>
</ul>
<ul>
<li><strong>BifTools [calcOneZeroEigenvalueBif]</strong> calculates the normal form of the steady states bifurcations with a single zero eigenvalue of the Jacobian;</li>
</ul>
<ul>
<li><strong>BifTools [calcHopfBifPoints]</strong> calculates the Andronov-Hopf bifurcation points of an ODE system, using the method of resultants;</li>
</ul>
<ul>
<li><strong>BifTools [calcHopfBif]</strong> calculates the normal form of the Andronov-Hopf bifurcation of the equilibrium points;</li>
</ul>
<ul>
<li><strong>BifTools [calcBTBif]</strong> calculates the normal form of the Bogdanov-Takens (double zero) bifurcation, using the projection or the direct method for center manifold reduction.</li>
</ul><img src="/view.aspx?si=128951/427373\BifTools.jpg" alt="BifTools - Package for Bifurcation Analysis in Dynamical Systems" align="left"/><p>BifTools is a package for symbolic and numeric bifurcation analysis of equilibrium points in dynamical systems. The package consists of five main procedures:</p>
<ul>
<li><strong>BifTools[calcOneZeroEigenvalueBifPoints]</strong> calculates the bifurcation points of an ODE system with a single zero eigenvalue of the Jacobian;</li>
</ul>
<ul>
<li><strong>BifTools [calcOneZeroEigenvalueBif]</strong> calculates the normal form of the steady states bifurcations with a single zero eigenvalue of the Jacobian;</li>
</ul>
<ul>
<li><strong>BifTools [calcHopfBifPoints]</strong> calculates the Andronov-Hopf bifurcation points of an ODE system, using the method of resultants;</li>
</ul>
<ul>
<li><strong>BifTools [calcHopfBif]</strong> calculates the normal form of the Andronov-Hopf bifurcation of the equilibrium points;</li>
</ul>
<ul>
<li><strong>BifTools [calcBTBif]</strong> calculates the normal form of the Bogdanov-Takens (double zero) bifurcation, using the projection or the direct method for center manifold reduction.</li>
</ul>128951Fri, 23 Dec 2011 05:00:00 ZNeli DimitrovaNeli DimitrovaAn Epidemic Model (for Influenza or Zombies)
http://www.maplesoft.com/applications/view.aspx?SID=127836&ref=Feed
<p>Systems of differential equations can be used to model an epidemic of influenza or of zombies. This is an interactive Maple document suitable for use in courses on mathematical biology or differential equations or calculus courses that include differential equations. No knowledge of Maple is required.</p><img src="/view.aspx?si=127836/Cholera.jpg" alt="An Epidemic Model (for Influenza or Zombies)" align="left"/><p>Systems of differential equations can be used to model an epidemic of influenza or of zombies. This is an interactive Maple document suitable for use in courses on mathematical biology or differential equations or calculus courses that include differential equations. No knowledge of Maple is required.</p>127836Thu, 17 Nov 2011 05:00:00 ZDr. Robert IsraelDr. Robert IsraelThe Orbit of Kepler 16b
http://www.maplesoft.com/applications/view.aspx?SID=126766&ref=Feed
<p>NASA's Kepler space telescope recently made the news by finding a planet that orbits a double-star system, a situation that brought to mind the fictional planet Tatooine of the movie Star Wars. On such a planet, if it had a solid surface, you could see a double sunset. <br /><br />This worksheet explores the orbital mechanics of such a system.</p><img src="/view.aspx?si=126766/kepler16b.png" alt="The Orbit of Kepler 16b" align="left"/><p>NASA's Kepler space telescope recently made the news by finding a planet that orbits a double-star system, a situation that brought to mind the fictional planet Tatooine of the movie Star Wars. On such a planet, if it had a solid surface, you could see a double sunset. <br /><br />This worksheet explores the orbital mechanics of such a system.</p>126766Tue, 18 Oct 2011 04:00:00 ZDr. Robert IsraelDr. Robert IsraelVarInt
http://www.maplesoft.com/applications/view.aspx?SID=88830&ref=Feed
<p><strong>VarInt</strong> - <em>Computer Algebra Aided Design of Variational Integrators</em>.</p>
<p>Create, design and analyse (new) variational integrators for autonomous dynamical systems (with non-conservative forces) up to arbitary order with VarInt, a package for Maple.</p><img src="/view.aspx?si=88830/VarIntSmall.jpg" alt="VarInt" align="left"/><p><strong>VarInt</strong> - <em>Computer Algebra Aided Design of Variational Integrators</em>.</p>
<p>Create, design and analyse (new) variational integrators for autonomous dynamical systems (with non-conservative forces) up to arbitary order with VarInt, a package for Maple.</p>88830Tue, 25 Jan 2011 05:00:00 ZChristian HellströmChristian HellströmAttracteurs de Gumowski-Mira
http://www.maplesoft.com/applications/view.aspx?SID=87666&ref=Feed
<p class="MsoNormal">En 1980, deux physiciens I. Gumowski et C. Mira, du centre de recherche CERN de Genève en Suisse utilisèrent le système d'équation</p>
<p class="MsoNormal"><span> </span>x<sub>n+1</sub> = By<sub>n</sub> + f(x<sub>n</sub>)<sub><o:p></o:p></sub></p>
<p class="MsoNormal"><span> </span>y<sub>n+1</sub> = - x<sub>n</sub> + f(x<sub>n+1</sub>)</p>
<p class="MsoNormal"><span> </span>où f(x) = Ax + 2(1 - A) x<sup>2</sup> / (1 + x<sup>2</sup>) et A, B sont des constantes.</p>
<p><span>pour simuler la trajectoire de particules se déplaçant à haute vitesse dans un accélérateur de la forme d'une mince boîte cylindrique de plusieurs mètres de long. Ils découvrirent à leur grande surprise </span><span>que les trajectoires issues de ce système et portées sur un plan cartésien produisent des images surprenantes.</span></p><img src="/view.aspx?si=87666/G_M.png" alt="Attracteurs de Gumowski-Mira" align="left"/><p class="MsoNormal">En 1980, deux physiciens I. Gumowski et C. Mira, du centre de recherche CERN de Genève en Suisse utilisèrent le système d'équation</p>
<p class="MsoNormal"><span> </span>x<sub>n+1</sub> = By<sub>n</sub> + f(x<sub>n</sub>)<sub><o:p></o:p></sub></p>
<p class="MsoNormal"><span> </span>y<sub>n+1</sub> = - x<sub>n</sub> + f(x<sub>n+1</sub>)</p>
<p class="MsoNormal"><span> </span>où f(x) = Ax + 2(1 - A) x<sup>2</sup> / (1 + x<sup>2</sup>) et A, B sont des constantes.</p>
<p><span>pour simuler la trajectoire de particules se déplaçant à haute vitesse dans un accélérateur de la forme d'une mince boîte cylindrique de plusieurs mètres de long. Ils découvrirent à leur grande surprise </span><span>que les trajectoires issues de ce système et portées sur un plan cartésien produisent des images surprenantes.</span></p>87666Sun, 16 May 2010 04:00:00 ZAndre LevesqueAndre LevesqueDynamical Systems with Applications using Maple
http://www.maplesoft.com/applications/view.aspx?SID=1701&ref=Feed
<p>Companion software for "Dynamical Systems with Applications using Maple 2nd Edition", Birkhäuser (2009). ISBN 978-0-8176-4389-8.</p>
<P><A HREF="http://www.maplesoft.com/books/books_detail.aspx?sid=102355">More information about this book is available here</A>.</P><img src="/view.aspx?si=1701/thumb.jpg" alt="Dynamical Systems with Applications using Maple" align="left"/><p>Companion software for "Dynamical Systems with Applications using Maple 2nd Edition", Birkhäuser (2009). ISBN 978-0-8176-4389-8.</p>
<P><A HREF="http://www.maplesoft.com/books/books_detail.aspx?sid=102355">More information about this book is available here</A>.</P>1701Thu, 08 Oct 2009 04:00:00 ZDr. Stephen LynchDr. Stephen LynchOptimal Control Design of a Voice Coil Actuator Head in a Hard Drive
http://www.maplesoft.com/applications/view.aspx?SID=6877&ref=Feed
<p>This document examines the steps involved in quickly and accurately controlling the position of the voice coil actuator head. The design of the closed-loop system, including the approach used to investigate the dynamics of the plant model and design the mathematical model of the controller, will be explained in detail.</p><img src="/view.aspx?si=6877/thumb.jpg" alt="Optimal Control Design of a Voice Coil Actuator Head in a Hard Drive" align="left"/><p>This document examines the steps involved in quickly and accurately controlling the position of the voice coil actuator head. The design of the closed-loop system, including the approach used to investigate the dynamics of the plant model and design the mathematical model of the controller, will be explained in detail.</p>6877Sun, 09 Nov 2008 05:00:00 ZMaplesoftMaplesoftControl Systems Design Tools: Creating and Working with System Objects
http://www.maplesoft.com/applications/view.aspx?SID=6587&ref=Feed
Maple provides a series of controls systems design tools that give you the ability to work analytically with linear time-invariant dynamic systems. The DynamicSystems package is a collection of procedures for creating, manipulating, simulating, and plotting linear time-invariant systems models. In this Tips and Techniques, you will learn how linear systems are modeled using the DynamicSystems package, how to create System Objects, and how to transform your models between a variety of different representations.<img src="/view.aspx?si=6587/TransferFunction.JPG" alt="Control Systems Design Tools: Creating and Working with System Objects" align="left"/>Maple provides a series of controls systems design tools that give you the ability to work analytically with linear time-invariant dynamic systems. The DynamicSystems package is a collection of procedures for creating, manipulating, simulating, and plotting linear time-invariant systems models. In this Tips and Techniques, you will learn how linear systems are modeled using the DynamicSystems package, how to create System Objects, and how to transform your models between a variety of different representations.6587Thu, 28 Aug 2008 00:00:00 ZMaplesoftMaplesoftFrequency Domain System Identification
http://www.maplesoft.com/applications/view.aspx?SID=1460&ref=Feed
System identification deals with the problem of identifying a model describing some physical system by measuring the response of the system. This example illustrates a problem where the structure of the model is known, and parameters of the model are identified. This is done by first designing the input signal, which is applied to the system. The measured output is converted to the frequency domain and the parameters are estimated in this domain.<img src="/view.aspx?si=1460/thumb.gif" alt="Frequency Domain System Identification" align="left"/>System identification deals with the problem of identifying a model describing some physical system by measuring the response of the system. This example illustrates a problem where the structure of the model is known, and parameters of the model are identified. This is done by first designing the input signal, which is applied to the system. The measured output is converted to the frequency domain and the parameters are estimated in this domain.1460Tue, 06 May 2008 00:00:00 ZMaplesoftMaplesoftDynamics in Spherical Coordinates
http://www.maplesoft.com/applications/view.aspx?SID=4892&ref=Feed
A brief introduction to dynamics in spherical coordinates.<img src="/view.aspx?si=4892/Dynamics in Spherical Coords Sketch 1.jpg" alt="Dynamics in Spherical Coordinates" align="left"/>A brief introduction to dynamics in spherical coordinates.4892Thu, 05 Apr 2007 00:00:00 ZJ. M. RedwoodJ. M. RedwoodStandard Map on a Torus
http://www.maplesoft.com/applications/view.aspx?SID=1703&ref=Feed
Maple worksheet for producing a standard map on a torus is developed. A brief introduction of Hamiltonian mechanics using a simple pendulum system as an example is provided, followed by a discussion of a kicked rotor system which consists of a simple pendulum with the potential energy turned on in delta-function pulses. The integration of the kicked rotor problem yields the standard map, which has characteristics of a large class of systems. Plotting the standard map on a torus facilitates a three-dimensional visualization the Kolmogorov-Arnold-Moser (KAM) theory of chaos in a Hamiltonian system. An animation demonstrating chaos created by homoclinic tangle near a hyperbolic point is contained in this worksheet.<img src="/view.aspx?si=1703/SMTorus.jpg" alt="Standard Map on a Torus" align="left"/>Maple worksheet for producing a standard map on a torus is developed. A brief introduction of Hamiltonian mechanics using a simple pendulum system as an example is provided, followed by a discussion of a kicked rotor system which consists of a simple pendulum with the potential energy turned on in delta-function pulses. The integration of the kicked rotor problem yields the standard map, which has characteristics of a large class of systems. Plotting the standard map on a torus facilitates a three-dimensional visualization the Kolmogorov-Arnold-Moser (KAM) theory of chaos in a Hamiltonian system. An animation demonstrating chaos created by homoclinic tangle near a hyperbolic point is contained in this worksheet.1703Tue, 10 Jan 2006 00:00:00 ZDr. Frank WangDr. Frank WangCreating an Animation of a Spatial Crank-Slider Mechanism using DynaFlexPro and Maple
http://www.maplesoft.com/applications/view.aspx?SID=1681&ref=Feed
The following Maple Worksheet details the steps involved in creating an animation of a Spatial Crank-Slider Mechanism using Maple 10 and DynaFlexPro, a third party product offering from Maplesoft.<img src="/view.aspx?si=1681/Slider 3D - spatial.JPG" alt="Creating an Animation of a Spatial Crank-Slider Mechanism using DynaFlexPro and Maple" align="left"/>The following Maple Worksheet details the steps involved in creating an animation of a Spatial Crank-Slider Mechanism using Maple 10 and DynaFlexPro, a third party product offering from Maplesoft.1681Tue, 08 Nov 2005 00:00:00 ZMaplesoftMaplesoftMobile Robot Modeling and Simulation
http://www.maplesoft.com/applications/view.aspx?SID=1467&ref=Feed
<p>Derive the model of a two wheel differential drive mobile robot and simulate its trajectory response to various inputs. A 3-D trajectory animation of the mobile robot has been created (shown above) based on the open loop system response of the derived mobile robot model. Various open loop and closed loop responses of this system have been generated in a separate application example application entitled, <a href="/applications/view.aspx?SID=1466" >Mobile Robot</a>.</p><img src="/view.aspx?si=1467/MobileRobotModel_3.gif" alt="Mobile Robot Modeling and Simulation" align="left"/><p>Derive the model of a two wheel differential drive mobile robot and simulate its trajectory response to various inputs. A 3-D trajectory animation of the mobile robot has been created (shown above) based on the open loop system response of the derived mobile robot model. Various open loop and closed loop responses of this system have been generated in a separate application example application entitled, <a href="/applications/view.aspx?SID=1466" >Mobile Robot</a>.</p>1467Mon, 16 May 2005 04:00:00 ZMaplesoftMaplesoft