Physics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=183
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 28 Oct 2016 10:21:28 GMTFri, 28 Oct 2016 10:21:28 GMTNew applications in the Physics categoryhttp://www.mapleprimes.com/images/mapleapps.gifPhysics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=183
Digitizing mathematics: ODEs, Special Functions and Solutions to Einstein's Equations
http://www.maplesoft.com/applications/view.aspx?SID=154174&ref=Feed
The material below was presented in the <A HREF="https://www.fields.utoronto.ca/programs/scientific/15-16/semantic/">Semantic Representation of Mathematical Knowledge Workshop</A>, February 3-5, 2016 at the Fields Institute, University of Toronto. It shows the approach used for “digitizing mathematical knowledge" regarding Differential Equations, Special Functions and Solutions to Einstein's equations. While for these areas using databases of information helps (for example textbooks frequently contain these sort of databases), these are areas that, at the same time, are very suitable for using algorithmic mathematical approaches, that result in much richer mathematics than what can be hard-coded into a database. The material also focuses on an interesting cherry-picked collection of Maple functionality, that I think is beautiful, not well know, and seldom focused inter-related as here.<BR><BR>
This application is also featured in a <A HREF="http://www.mapleprimes.com/posts/206715-Digitizing-Mathematics-ODEs-Special">MaplePrimes blog post</A>.<img src="/applications/images/app_image_blank_lg.jpg" alt="Digitizing mathematics: ODEs, Special Functions and Solutions to Einstein's Equations" align="left"/>The material below was presented in the <A HREF="https://www.fields.utoronto.ca/programs/scientific/15-16/semantic/">Semantic Representation of Mathematical Knowledge Workshop</A>, February 3-5, 2016 at the Fields Institute, University of Toronto. It shows the approach used for “digitizing mathematical knowledge" regarding Differential Equations, Special Functions and Solutions to Einstein's equations. While for these areas using databases of information helps (for example textbooks frequently contain these sort of databases), these are areas that, at the same time, are very suitable for using algorithmic mathematical approaches, that result in much richer mathematics than what can be hard-coded into a database. The material also focuses on an interesting cherry-picked collection of Maple functionality, that I think is beautiful, not well know, and seldom focused inter-related as here.<BR><BR>
This application is also featured in a <A HREF="http://www.mapleprimes.com/posts/206715-Digitizing-Mathematics-ODEs-Special">MaplePrimes blog post</A>.154174Fri, 07 Oct 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-TerrabEquivalence problem in General Relativity
http://www.maplesoft.com/applications/view.aspx?SID=154159&ref=Feed
In this presentation, the equivalence problem for Schwarzschild metric in a simple case is formulated and solved to the end using the <A HREF="/support/help/Maple/view.aspx?path=PDEtools">PDEtools</A>, <A HREF="/support/help/Maple/view.aspx?path=physics">Physics</A> and <A HREF="/support/help/maple/view.aspx?path=Physics/Tetrads">Physics:-Tetrads</A> Maple packages.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203426-Equivalence-Problem-In-General-Relativity">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154159/quantum.jpg" alt="Equivalence problem in General Relativity" align="left"/>In this presentation, the equivalence problem for Schwarzschild metric in a simple case is formulated and solved to the end using the <A HREF="/support/help/Maple/view.aspx?path=PDEtools">PDEtools</A>, <A HREF="/support/help/Maple/view.aspx?path=physics">Physics</A> and <A HREF="/support/help/maple/view.aspx?path=Physics/Tetrads">Physics:-Tetrads</A> Maple packages.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203426-Equivalence-Problem-In-General-Relativity">blog post on MaplePrimes</A>.154159Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabExact solutions to Einstein's equations
http://www.maplesoft.com/applications/view.aspx?SID=154161&ref=Feed
The Maple database of solutions to Einstein’s equations, constructed digitizing the solutions found in the book “Exact Solutions of Einstein's Field Equations” by Stephani et al. is presented.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201548-Exact-Solutions-To-Einsteins-Equations">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154161/Einstein.jpg" alt="Exact solutions to Einstein's equations" align="left"/>The Maple database of solutions to Einstein’s equations, constructed digitizing the solutions found in the book “Exact Solutions of Einstein's Field Equations” by Stephani et al. is presented.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201548-Exact-Solutions-To-Einsteins-Equations">blog post on MaplePrimes</A>.154161Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabGeneral Relativity using Computer Algebra
http://www.maplesoft.com/applications/view.aspx?SID=154163&ref=Feed
This presentation illustrates the use of the functionality of the Physics package for General Relativity in tackling part of the computations of a paper in General Relativity from 2013, mainly about computing a complicated tensorial expression, calculating its trace, then the related traceless expression and finally an exact solution to the corresponding system of nonlinear differential equations.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200192-General-Relativity-Using-Computer-Algebra">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154163/theoreticalphysics.jpg" alt="General Relativity using Computer Algebra" align="left"/>This presentation illustrates the use of the functionality of the Physics package for General Relativity in tackling part of the computations of a paper in General Relativity from 2013, mainly about computing a complicated tensorial expression, calculating its trace, then the related traceless expression and finally an exact solution to the corresponding system of nonlinear differential equations.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200192-General-Relativity-Using-Computer-Algebra">blog post on MaplePrimes</A>.154163Fri, 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.
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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.
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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-TerrabThe 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.
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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.
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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.
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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.
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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-TerrabTetrads and Weyl scalars in canonical form
http://www.maplesoft.com/applications/view.aspx?SID=154160&ref=Feed
This presentation is about the computation of a canonical form of a tetrad, so that, generally speaking (skipping a technical description) the Weyl scalars are fixed as much as possible (either equal to 0 or to 1) regarding transformations that leave invariant the tetrad metric in a tetrad system of references. Bringing a tetrad in canonical form is a relevant step in the tackling of the equivalence problem between two spacetime metrics (solutions to Einstein's equations).<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203425-Tetrads-And-Weyl-Scalars-In-Canonical-Form">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154160/theoreticalphysics.jpg" alt="Tetrads and Weyl scalars in canonical form" align="left"/>This presentation is about the computation of a canonical form of a tetrad, so that, generally speaking (skipping a technical description) the Weyl scalars are fixed as much as possible (either equal to 0 or to 1) regarding transformations that leave invariant the tetrad metric in a tetrad system of references. Bringing a tetrad in canonical form is a relevant step in the tackling of the equivalence problem between two spacetime metrics (solutions to Einstein's equations).<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203425-Tetrads-And-Weyl-Scalars-In-Canonical-Form">blog post on MaplePrimes</A>.154160Fri, 30 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-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.
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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/theoreticalphysics2.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.
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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-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/vp.png" 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.
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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 Baroudy