Fixed Final Time: Second Differential

  • David G. Hull
Part of the Mechanical Engineering Series book series (MES)


In this chapter, the second differential is investigated to obtain the LegendreClebsch condition and the Jacobi or conjugate point condition. First, the second differential is obtained by taking the differential of the first differential. Second, the Legendre-Clebsch condition is derived from the second differential. Third, for the class of nonsingular problems (H uu > 0) conditions are developed for the existence of a neighboring optimal path. Finally, these conditions are used to develop a sufficient condition for the existence of a weak relative minimum.


Performance Index Optimal Path Great Circle Conjugate Point North Pole 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • David G. Hull
    • 1
  1. 1.Aerospace Engineering and Engineering MechanicsThe University of Texas at AustinAustinUSA

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