Abstract
The transition from (what is here called) the mechanics of Lagrange, with time as the main parameter, to the mechanics of Hamilton and Jacobi, with energy as the controlling variable, is formally easy to carry out. Its importance becomes apparent when one tries to solve special problems. The test case is the motion of a body where the force decreases as the inverse square of the distance from the origin. It will be treated at the end of this chapter and will be given an appealing geometrical solution.
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© 1990 Springer Science+Business Media New York
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Gutzwiller, M.C. (1990). The Mechanics of Hamilton and Jacobi. In: Chaos in Classical and Quantum Mechanics. Interdisciplinary Applied Mathematics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0983-6_3
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DOI: https://doi.org/10.1007/978-1-4612-0983-6_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6970-0
Online ISBN: 978-1-4612-0983-6
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