Module 7: Two Dimensional Nonlinear Dynamic Systems

Folder description

Please click the folder link above to access the Module 7 instructional content. Module 7 contains the following:

  • 07A: Example
  • 07B: Example
  • 07C: Hamiltonian Systems
  • 07D: Time Reversible Systems
  • 07E: Pendulum
  • 07F: Pendulum with Damping
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Module at a Glance

Cell description

In this module we'll continue developing an understanding of nonlinear dynamical systems using physical examples.

Objectives

  • By the end of this module, you will be able to:
  • Examine the dynamics that arise from conservative systems.
  • Analyze systems with symmetry in time.
  • Evaluate a pendulum system using phase plane methods.
  • Examine the n-body problem.

How to complete this module:

  1. Watch the video lectures 7A through 7F. 
  2. Complete the reading assignment.
  3. Respond to the discussion board question.
  4. Complete the assignment.
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Readings

Cell description

This week's reading assignment includes the following:

  • Strogatz, Steven HNonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and EngineeringCRC Press, 2018. 
    • Chapter 6 (pp. 160-180) 
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Module 7 Discussion

Cell description

Endure as much of this video as you can about the n-body problem. Then watch the various demonstrations of n-body dynamics. Based on the dynamics, can you describe the behavior of a phase portrait? Comment on at least two other student described applications.

You may access the discussion forum by selecting the link above or by going to the discussion area from the left menu bar.

Name: Orbital Dynamics Part 57 -- The N Body Problem
Duration:  
Added: 12 Aug 2019 07:55 AM
Added By: DIANE BANNER
Description:  
Tags: 625.718.31, stein

Due: Sunday 11:59 pm

 

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Then watch the various demonstrations of n-body dynamics. Based on the dynamics, can you describe the behavior of a phase portrait? 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clear: right;\"> \n    <table style=\"margin: 0px !important; border-collapse: collapse;\"> \n     <tbody> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\"><b>Name:</b></td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\"><b>Orbital Dynamics Part 57 -- The N Body Problem</b></td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Duration:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">12 Aug 2019 07:55 AM</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added By:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">DIANE BANNER</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Description:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Tags:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">625.718.31, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <div style=\"width: 604px; overflow: hidden;\"> \n  <div style=\"float: left; clear: left;\"> \n   <div style=\"float: left; clear: both;\"></div> \n  </div> \n </div> \n <div style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal !important;\"> \n  <strong style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: inherit; font-size: 13px;\"><span data-contrast=\"auto\" xml:lang=\"EN-US\" style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></span></strong> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: normal; font-size: 13px; color: #000000; 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Then watch the various demonstrations of n-body dynamics. Based on the dynamics, can you describe the behavior of a phase portrait? Comment on at least two other student described applications.</p> \n <p>You may access the discussion forum by selecting the link above or by going to the discussion area from the left menu bar.</p> \n <div style=\"width: 604px; overflow: hidden;\"> \n  <div style=\"float: left; clear: left;\"> \n   <div style=\"float: left; clear: both;\"> \n    <iframe width=\"320\" height=\"240\" style=\"width: 604px; height: 386px;\" frameborder=\"0\" scrolling=\"no\" allowfullscreen=\"true\" allow=\"autoplay *; fullscreen *; encrypted-media *; camera *; microphone *;\" src=\"/webapps/osv-kaltura-bb_bb60/content/iframe.jsp?url=..%2FLtiMashupPlayIframeWrapperResponsive%3FplayUrl%3D%2Fbrowseandembed%2Findex%2Fmedia%2Fentryid%2F0_v1177b71%2FshowDescription%2Ffalse%2FshowTitle%2Ffalse%2FshowTags%2Ffalse%2FshowDuration%2Ffalse%2FshowOwner%2Ffalse%2FshowUploadDate%2Ffalse%2FplayerSize%2F400x285%2FplayerSkin%2F30749451%2F&amp;thumbnail=https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/0_v1177b71/version/100002&amp;title=Orbital+Dynamics+Part+57+--+The+N+Body+Problem&amp;course_id=_194578_1&amp;content_id=_7048769_1\"></iframe> \n   </div> \n  </div> \n  <div id=\"container_0.12093083351198985\" class=\"hide-icon hidden\" style=\"margin-top: 30px; float: left; clear: left;\"> \n   <div style=\"float: left; clear: left; margin-right: 8px;\"> \n    <div style=\"float: left; clear: both;\"> \n     <a class=\"lb\" style=\"text-decoration: none; color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_v1177b71/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Orbital Dynamics Part 57 -- The N Body Problem\"> <img border=\"0\" src=\"https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/0_v1177b71/version/100002\"> </a> \n    </div> \n    <div style=\"float: left; clear: both; width: 100%; background: url('/images/ci/ng/rumble_button_back.gif') 50% 50%; padding-top: 2px; padding-bottom: 2px; text-decoration: none; color: #333333; text-align: center;\"> \n     <a class=\"lb\" style=\"text-decoration: none; color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_v1177b71/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Orbital Dynamics Part 57 -- The N Body Problem\"> Watch Media </a> \n    </div> \n   </div> \n   <div style=\"float: left; clear: right;\"> \n    <table style=\"margin: 0px !important; border-collapse: collapse;\"> \n     <tbody> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\"><b>Name:</b></td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\"><b>Orbital Dynamics Part 57 -- The N Body Problem</b></td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Duration:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">12 Aug 2019 07:55 AM</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added By:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">DIANE BANNER</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Description:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Tags:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">625.718.31, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <div style=\"width: 604px; overflow: hidden;\"> \n  <div style=\"float: left; clear: left;\"> \n   <div style=\"float: left; clear: both;\"></div> \n  </div> \n </div> \n <div style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal !important;\"> \n  <strong style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: inherit; font-size: 13px;\"><span data-contrast=\"auto\" xml:lang=\"EN-US\" style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></span></strong> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: normal; font-size: 13px; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">Due: Sunday 11:59 pm</strong></p> \n <p style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></p> \n <p><strong>&nbsp;</strong></p> \n <p><br></p> \n</div>\n  </div>\n\n <div id=\"_7048769_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Module 7 Discussion",
        "body": "\n    <div> \n <p>Endure as much of this video as you can about the n-body problem. Then watch the various demonstrations of n-body dynamics. Based on the dynamics, can you describe the behavior of a phase portrait? Comment on at least two other student described applications.</p> \n <p>You may access the discussion forum by selecting the link above or by going to the discussion area from the left menu bar.</p> \n <div> \n  <div> \n   <div> \n     \n   </div> \n  </div> \n  <div id=\"container_0.12093083351198985\"> \n   <div> \n    <div> \n     <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_v1177b71/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Orbital Dynamics Part 57 -- The N Body Problem\">  </a> \n    </div> \n    <div> \n     <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_v1177b71/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Orbital Dynamics Part 57 -- The N Body Problem\"> Watch Media </a> \n    </div> \n   </div> \n   <div> \n    <table> \n     <tbody> \n      <tr> \n       <td><b>Name:</b></td> \n       <td><b>Orbital Dynamics Part 57 -- The N Body Problem</b></td> \n      </tr> \n      <tr> \n       <td>Duration:</td> \n       <td>&nbsp;</td> \n      </tr> \n      <tr> \n       <td>Added:</td> \n       <td>12 Aug 2019 07:55 AM</td> \n      </tr> \n      <tr> \n       <td>Added By:</td> \n       <td>DIANE BANNER</td> \n      </tr> \n      <tr> \n       <td>Description:</td> \n       <td>&nbsp;</td> \n      </tr> \n      <tr> \n       <td>Tags:</td> \n       <td>625.718.31, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <div> \n  <div> \n    \n  </div> \n </div> \n <div> \n   \n </div> \n <p><strong>Due: Sunday 11:59 pm</strong></p> \n  \n <p><strong>&nbsp;</strong></p> \n  \n</div>\n  "
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Module 7 Assignment

Cell description
  • Complete the following problems from chapter 6 of the Strogatz textbook: 6.5.1 (7 pts.); 6.5.2 (7 pts.); 6.5.9 (3 pts.); 6.6.1 (5 pts.); 6.7.2 (10 pts.)
  • Upload your work in PDF format by selecting the link above.

Due: Tuesday 11:59 pm

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