Other: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=183
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 19 Feb 2017 23:19:58 GMTSun, 19 Feb 2017 23:19:58 GMTNew applications in the Other categoryhttp://www.mapleprimes.com/images/mapleapps.gifOther: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=183
The Gross-Pitaevskii equation and Bogoliubov spectrum
http://www.maplesoft.com/applications/view.aspx?SID=154155&ref=Feed
The spectrum of its solutions of the equation for a quantum system of identical particles, that is the Gross-Pitaevskii equation (GPE) is derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200120-Quantum-Mechanics-II">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154155/theoreticalphysics.jpg" alt="The Gross-Pitaevskii equation and Bogoliubov spectrum" align="left"/>The spectrum of its solutions of the equation for a quantum system of identical particles, that is the Gross-Pitaevskii equation (GPE) is derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200120-Quantum-Mechanics-II">blog post on MaplePrimes</A>.154155Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabQuantization of the Lorentz Force
http://www.maplesoft.com/applications/view.aspx?SID=154168&ref=Feed
Departing from the Hamiltonian of a quantum, non-relativistic, particle with mass m and charge q, evolving under the action of an arbitrary time-independent matgnetic field, derive the expression of the quantized Lorentz force.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/206511-Quantization-Of-The-Lorentz-Force">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154168/quantum.jpg" alt="Quantization of the Lorentz Force" align="left"/>Departing from the Hamiltonian of a quantum, non-relativistic, particle with mass m and charge q, evolving under the action of an arbitrary time-independent matgnetic field, derive the expression of the quantized Lorentz force.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/206511-Quantization-Of-The-Lorentz-Force">blog post on MaplePrimes</A>.154168Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabComputer Algebra in Theoretical Physics (IOP Webinar)
http://www.maplesoft.com/applications/view.aspx?SID=154157&ref=Feed
Recent advancements in computational physics are illustrated, showing how these techniques can be applied to problems from general relativity, classical mechanics, quantum mechanics, and classical field theory, including the presentation of the digitization of the solutions to Einstein’s field equations shown in the book “Exact Solutions to Einstein’s Field Equations”.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203574-Computer-Algebra-In-Theoretical-Physics">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154157/theoreticalphysics.jpg" alt="Computer Algebra in Theoretical Physics (IOP Webinar)" align="left"/>Recent advancements in computational physics are illustrated, showing how these techniques can be applied to problems from general relativity, classical mechanics, quantum mechanics, and classical field theory, including the presentation of the digitization of the solutions to Einstein’s field equations shown in the book “Exact Solutions to Einstein’s Field Equations”.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203574-Computer-Algebra-In-Theoretical-Physics">blog post on MaplePrimes</A>.154157Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabMini-Course: Computer Algebra for Physicists
http://www.maplesoft.com/applications/view.aspx?SID=154158&ref=Feed
This is a course, organized as a guided experience, 2 hours per day during five days, on learning the basics of the Maple language, and on using it to formulate algebraic computations we do in physics with paper and pencil. It is oriented to people not familiar with computer algebra (sections 1-5), as well as to people who are familiar but want to learn more about how to use it in Physics.<img src="/view.aspx?si=154158/physicscourse.PNG" alt="Mini-Course: Computer Algebra for Physicists" align="left"/>This is a course, organized as a guided experience, 2 hours per day during five days, on learning the basics of the Maple language, and on using it to formulate algebraic computations we do in physics with paper and pencil. It is oriented to people not familiar with computer algebra (sections 1-5), as well as to people who are familiar but want to learn more about how to use it in Physics.154158Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabGround state of a quantum system of identical boson particles
http://www.maplesoft.com/applications/view.aspx?SID=154156&ref=Feed
Departing from the Energy of a quantum system of identical boson particles, the field equation, that is the Gross-Pitaevskii equation, is derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200109-Quantum-Mechanics-Using-Computer-Algebra">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154156/quantum.jpg" alt="Ground state of a quantum system of identical boson particles" align="left"/>Departing from the Energy of a quantum system of identical boson particles, the field equation, that is the Gross-Pitaevskii equation, is derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200109-Quantum-Mechanics-Using-Computer-Algebra">blog post on MaplePrimes</A>.154156Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabFactorizing with non-commutative variables
http://www.maplesoft.com/applications/view.aspx?SID=154166&ref=Feed
New capabilities for factorizing expressions involving noncommutative variables are presented and illustrated with a set of examples.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201368-New-Factorizing-With-Noncommutative-Variables">blog post on MaplePrimes</A>.<img src="/applications/images/app_image_blank_lg.jpg" alt="Factorizing with non-commutative variables" align="left"/>New capabilities for factorizing expressions involving noncommutative variables are presented and illustrated with a set of examples.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201368-New-Factorizing-With-Noncommutative-Variables">blog post on MaplePrimes</A>.154166Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabQuantum Mechanics: Schrödinger vs Heisenberg picture
http://www.maplesoft.com/applications/view.aspx?SID=154153&ref=Feed
Departing from the Shrodinger picture of Quantum Mechanics, the Heisenberg picture and related formulas are derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/205867-Quantum-Mechanics-Schrdinger-Vs-Heisenberg">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154153/theoreticalphysicsThumb.jpg" alt="Quantum Mechanics: Schrödinger vs Heisenberg picture" align="left"/>Departing from the Shrodinger picture of Quantum Mechanics, the Heisenberg picture and related formulas are derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/205867-Quantum-Mechanics-Schrdinger-Vs-Heisenberg">blog post on MaplePrimes</A>.154153Thu, 29 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabThe Landau criterion for Superfluidity
http://www.maplesoft.com/applications/view.aspx?SID=154154&ref=Feed
The conditions for superfluidity of a system of identical particles at low temperature are derived.<BR><BR>This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200240-Superfluidity-In-Quantum-Mechanics">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154154/quantummechanics.jpg" alt="The Landau criterion for Superfluidity" align="left"/>The conditions for superfluidity of a system of identical particles at low temperature are derived.<BR><BR>This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200240-Superfluidity-In-Quantum-Mechanics">blog post on MaplePrimes</A>.154154Thu, 29 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabVectors in the plane.
http://www.maplesoft.com/applications/view.aspx?SID=154071&ref=Feed
If an object is subjected to several forces having different magnitudes and act in different directions, how can determine the magnitude and direction of the resultant total force on the object? Forces are vectors and should be added according to the definition of the vector sum. Engineering dealing with many quantities that have both magnitude and direction and can be expressed and analyzed as vectors.
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In Spanish.<img src="/view.aspx?si=154071/vpThumb.jpg" alt="Vectors in the plane." align="left"/>If an object is subjected to several forces having different magnitudes and act in different directions, how can determine the magnitude and direction of the resultant total force on the object? Forces are vectors and should be added according to the definition of the vector sum. Engineering dealing with many quantities that have both magnitude and direction and can be expressed and analyzed as vectors.
<BR><BR>
In Spanish.154071Fri, 01 Apr 2016 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloBall Bouncing on Hilly Terrain
http://www.maplesoft.com/applications/view.aspx?SID=154003&ref=Feed
The following application demonstrates how event modeling in the dsolve command can be used to model a ball bouncing on a hilly terrain.<img src="/view.aspx?si=154003/hilly_terrain.png" alt="Ball Bouncing on Hilly Terrain" align="left"/>The following application demonstrates how event modeling in the dsolve command can be used to model a ball bouncing on a hilly terrain.154003Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanLattice: A package to model accelerator lattices and beam lines
http://www.maplesoft.com/applications/view.aspx?SID=153970&ref=Feed
The Lattice package is a Maple package to design and analyze charged-particle beam lines and circular machines. It employs a beam-line description using the standard elements (dipoles, quadrupoles and so on) and retains the algebraic power of Maple. Beam-line elements are described using the equations governing the particle motion in algebraic form. In this way it is possible to compute expressions for beam-line parameters like Twiss functions, dispersion and such, for beam
lines or rings, and to perform analysis on these expressions using the full power of Maple.<img src="/view.aspx?si=153970/Lattice.png" alt="Lattice: A package to model accelerator lattices and beam lines" align="left"/>The Lattice package is a Maple package to design and analyze charged-particle beam lines and circular machines. It employs a beam-line description using the standard elements (dipoles, quadrupoles and so on) and retains the algebraic power of Maple. Beam-line elements are described using the equations governing the particle motion in algebraic form. In this way it is possible to compute expressions for beam-line parameters like Twiss functions, dispersion and such, for beam
lines or rings, and to perform analysis on these expressions using the full power of Maple.153970Tue, 01 Mar 2016 05:00:00 ZUli WienandsUli WienandsGlobal Temperature Anomaly
http://www.maplesoft.com/applications/view.aspx?SID=153951&ref=Feed
The temperature anomaly or temperature index is defined as the change from a reference temperature or a long-term mean value. A positive ( negative) anomaly indicates that a measured temperuture is warmer (cooler) than the reference value. In this worksheet anomalies have been based upon the period between 1951 to 1980. We consider especially temperature change from 1980 to 2015.<img src="/view.aspx?si=153951/GlobalTemperature.png" alt="Global Temperature Anomaly" align="left"/>The temperature anomaly or temperature index is defined as the change from a reference temperature or a long-term mean value. A positive ( negative) anomaly indicates that a measured temperuture is warmer (cooler) than the reference value. In this worksheet anomalies have been based upon the period between 1951 to 1980. We consider especially temperature change from 1980 to 2015.153951Tue, 19 Jan 2016 05:00:00 ZProf. Josef BettenProf. Josef BettenFitting Wave Height Data to a Probability Distribution
http://www.maplesoft.com/applications/view.aspx?SID=153864&ref=Feed
<p>The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.</p>
<p>This application:</p>
<ul>
<li>downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W),</li>
</ul>
<ul>
<li>fits the significant wave height to a Weibull distribution via two methods: maximum likelihood estimation and moment matching,</li>
</ul>
<ul>
<li>and plots the fitted distributions on top of a histogram of the experimental data</li>
</ul>
<p>The location of buoy PR206 is given in a Google Maps component.</p><img src="/view.aspx?si=153864/distribution.jpg" alt="Fitting Wave Height Data to a Probability Distribution" align="left"/><p>The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.</p>
<p>This application:</p>
<ul>
<li>downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W),</li>
</ul>
<ul>
<li>fits the significant wave height to a Weibull distribution via two methods: maximum likelihood estimation and moment matching,</li>
</ul>
<ul>
<li>and plots the fitted distributions on top of a histogram of the experimental data</li>
</ul>
<p>The location of buoy PR206 is given in a Google Maps component.</p>153864Wed, 09 Sep 2015 04:00:00 ZSamir KhanSamir KhanTime Series Analysis: Forecasting Average Global Temperatures
http://www.maplesoft.com/applications/view.aspx?SID=153791&ref=Feed
Maple includes powerful tools for accessing, analyzing, and visualizing time series data. This application works with global temperature data to demonstrate techniques for analyzing time series data sets using the TimeSeriesAnalysis package, including visualizing trends and modeling future global temperatures.<img src="/view.aspx?si=153791/thumb.jpg" alt="Time Series Analysis: Forecasting Average Global Temperatures" align="left"/>Maple includes powerful tools for accessing, analyzing, and visualizing time series data. This application works with global temperature data to demonstrate techniques for analyzing time series data sets using the TimeSeriesAnalysis package, including visualizing trends and modeling future global temperatures.153791Tue, 21 Apr 2015 04:00:00 ZDaniel SkoogDaniel SkoogThe 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 BaroudyPhoton Exposure
http://www.maplesoft.com/applications/view.aspx?SID=153684&ref=Feed
<p>This application uses a blackbody model of the sun to calculate the number of photons reaching a cameras sensor. It demonstrates the "Sunny 16" model of exposure.</p><img src="/view.aspx?si=153684/e771d3d2526673d4a8bc8221b6d228ee.gif" alt="Photon Exposure" align="left"/><p>This application uses a blackbody model of the sun to calculate the number of photons reaching a cameras sensor. It demonstrates the "Sunny 16" model of exposure.</p>153684Mon, 29 Sep 2014 04:00:00 ZJohn DoleseJohn DoleseDescartes & 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 BaroudyMeasuring Water Flow of Rivers
http://www.maplesoft.com/applications/view.aspx?SID=153480&ref=Feed
In this guest article in the Tips & Techniques series, Dr. Michael Monagan discusses the art and science of measuring the amount of water flowing in a river, and relates his personal experiences with this task to its morph into a project for his calculus classes.<img src="/view.aspx?si=153480/thumb.jpg" alt="Measuring Water Flow of Rivers" align="left"/>In this guest article in the Tips & Techniques series, Dr. Michael Monagan discusses the art and science of measuring the amount of water flowing in a river, and relates his personal experiences with this task to its morph into a project for his calculus classes.153480Fri, 13 Dec 2013 05:00:00 ZProf. Michael MonaganProf. Michael MonaganSymmetry of two-dimensional hybrid metal-dielectric photonic crystal within MAPLE
http://www.maplesoft.com/applications/view.aspx?SID=151383&ref=Feed
<p>Hybrid structures were made by assembling monolayers (MLs) of closely packed colloidal microspheres on a metal-coated glass substrate . In fact, this architecture is one of several realizations of hybrid plasmonic-photonic crystals (PHs), which differ in photonic crystals dimensionality and metal ﬁlm corrugation [1,2].</p>
<p>The main challenge to us were exploring of those properties of structures which are caused by their space symmetry. In particular, it was necessary to establish the so-called "rules of selection", i.e. the list of the allowed transitions between electronic states of different symmetry and energy that can be induced by light of varying polarization. Additional interest for us was to demonstrate the possibilities of MAPLE within this specific field.</p><img src="/view.aspx?si=151383/440fb9a2994e797b26c18564d860131b.gif" alt="Symmetry of two-dimensional hybrid metal-dielectric photonic crystal within MAPLE" align="left"/><p>Hybrid structures were made by assembling monolayers (MLs) of closely packed colloidal microspheres on a metal-coated glass substrate . In fact, this architecture is one of several realizations of hybrid plasmonic-photonic crystals (PHs), which differ in photonic crystals dimensionality and metal ﬁlm corrugation [1,2].</p>
<p>The main challenge to us were exploring of those properties of structures which are caused by their space symmetry. In particular, it was necessary to establish the so-called "rules of selection", i.e. the list of the allowed transitions between electronic states of different symmetry and energy that can be induced by light of varying polarization. Additional interest for us was to demonstrate the possibilities of MAPLE within this specific field.</p>151383Thu, 05 Sep 2013 04:00:00 ZOlga V. DvornikOlga V. DvornikHohmann Elliptic Transfer Orbit with Animation
http://www.maplesoft.com/applications/view.aspx?SID=151351&ref=Feed
<p>Abstract<br /><br />The main purpose of this article is to show how to use Hohmann elliptic transfer in two situations:<br />a- When one manned spaceship is trying to catch up with an other one <br />on the same circular orbit around Earth.<br />b- When delivering a payload from Earth to a space station on a circular <br />orbit around Earth using 2-stage rocket .<br /><br />The way we set up the problem is as follows:<br />Consider two manned spaceships with astronauts Sally & Igor , the latter<br />lagging behind Sally by a given angle = 4.5 degrees while both are on the same<br />circular orbit C2 about Earth. A 2d lower circular orbit C1 is given. <br />Find the Hohmann elliptic orbit that is tangent to both orbits which allows<br />Sally to maneuver on C1 then to get back to the circular orbit C2 alongside Igor.<br /><br />Though the math was correct , however the final result we found was not !! <br />It was somehow tricky to find the culprit!<br />We have to restate the problem to get the correct answer. <br />The animation was then set up using the correct data. <br />The animation is a good teaching help for two reasons:<br />1- it gives a 'hand on' experience for anyone who wants to fully understand it,<br />2- it is a good lesson in Maple programming with many loops of the type 'if..then'.<br /><br />Warning<br /><br />This particular animation is a hog for the CPU memory since data accumulated <br />for plotting reached 20 MB! This is the size of this article when animation is <br />executed. For this reason and to be able to upload it I left the animation <br />procedure non executed which drops the size of the article to 300KB.<br /><br />Conclusion<br /><br />If I can get someone interested in the subject of this article in such away that he or <br />she would seek further information for learning from other sources, my efforts<br />would be well rewarded.</p><img src="/view.aspx?si=151351/24030360191a26b4d767de35f843bbd8.gif" alt="Hohmann Elliptic Transfer Orbit with Animation" align="left"/><p>Abstract<br /><br />The main purpose of this article is to show how to use Hohmann elliptic transfer in two situations:<br />a- When one manned spaceship is trying to catch up with an other one <br />on the same circular orbit around Earth.<br />b- When delivering a payload from Earth to a space station on a circular <br />orbit around Earth using 2-stage rocket .<br /><br />The way we set up the problem is as follows:<br />Consider two manned spaceships with astronauts Sally & Igor , the latter<br />lagging behind Sally by a given angle = 4.5 degrees while both are on the same<br />circular orbit C2 about Earth. A 2d lower circular orbit C1 is given. <br />Find the Hohmann elliptic orbit that is tangent to both orbits which allows<br />Sally to maneuver on C1 then to get back to the circular orbit C2 alongside Igor.<br /><br />Though the math was correct , however the final result we found was not !! <br />It was somehow tricky to find the culprit!<br />We have to restate the problem to get the correct answer. <br />The animation was then set up using the correct data. <br />The animation is a good teaching help for two reasons:<br />1- it gives a 'hand on' experience for anyone who wants to fully understand it,<br />2- it is a good lesson in Maple programming with many loops of the type 'if..then'.<br /><br />Warning<br /><br />This particular animation is a hog for the CPU memory since data accumulated <br />for plotting reached 20 MB! This is the size of this article when animation is <br />executed. For this reason and to be able to upload it I left the animation <br />procedure non executed which drops the size of the article to 300KB.<br /><br />Conclusion<br /><br />If I can get someone interested in the subject of this article in such away that he or <br />she would seek further information for learning from other sources, my efforts<br />would be well rewarded.</p>151351Wed, 04 Sep 2013 04:00:00 ZDr. Ahmed BaroudyDr. Ahmed Baroudy