Differential Equations Solutions 141

Differential Equations Solutions 141 - 1 V Arun The...

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Chapter 25 Solutions: Case Study: Variable-Geometry Trusses: What’s Your Angle? CHALLENGE 25.1. See Figures 25.1 – 25.4. CHALLENGE 25.2. See the programs on the website. CHALLENGE 25.3. See the programs on the website and the fgure in the book. Compare your results with Arun, who ±ound 8 solutions ±or Plat±orm A, 8 ±or Plat±orm B, 4 ±or Plat±orm C, and 16 ±or Plat±orm D. The continuation method was much slower than fsolve and gave no more solutions. A trick called homogenization can be used to improve the homotopy. This involves replacing the variables by their inverses in order to take solutions that are at infnity and map them to zero. See [1,2,3] ±or more details.
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Unformatted text preview: 1. V. Arun, The Solution of Variable-Geometry Truss Problems Using New Ho-motopy Continuation Methods , PhD thesis, Mechanical Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, Septem-ber 1990. 2. V. Arun, C. F. Reinholtz, and L. T. Watson, Application o± new homotopy continuation techniques to variable geometry trusses, Trans. of the ASME , 114:422– 428, September 1992. 3. A. Morgan, Solving Polynomial Systems Using Continuation For Engineering and Scienti±c Problems , Prentice-Hall, Englewood Cli²s, NJ, 1987. 151...
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