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- W2230723534 abstract "We have repeatedly emphasized that determining the explicit solutions of Hamiltonian equations is a task beyond the capabilities of mathematics. This situation justifies all attempts to obtain information about these solutions. For instance, a knowledge of the first integrals allows us to localize the dynamical trajectories in the phase space M 2n ∗. In turn, Nother’s theorem proves that the presence of first integrals is strictly related to the existence of symmetries. In this chapter, we analyze the Hamilton–Jacobi theory whose purpose it is to determine a set of canonical coordinates in which the Hamiltonian equations have such a simple form that we can obtain solutions without effort. However, determining this set of coordinates requires solving a nonlinear partial differential equation. Although, in general, this problem could be more difficult than the direct integration of the Hamiltonian equations, there are some interesting cases in which we are able to exhibit its solution by adopting the method, proposed by Jacobi, of separated variables." @default.
- W2230723534 created "2016-06-24" @default.
- W2230723534 creator A5015945494 @default.
- W2230723534 date "2012-01-01" @default.
- W2230723534 modified "2023-09-23" @default.
- W2230723534 title "The Hamilton-Jacobi Theory" @default.
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- W2230723534 doi "https://doi.org/10.1007/978-0-8176-8352-8_19" @default.
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