The Mechanics of Hamilton and Jacobi
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.
KeywordsPhase Space Position Space Semimajor Axis Conjugate Point Legendre Transformation
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