Generation of solutions of the Hamilton--Jacobi equation

Authors

  • G.F. Torres del Castillo

Keywords:

Hamilton--Jacobi equation, canonical transformations, constants of motion

Abstract

It is shown that any function $G(q_{i}, p_{i}, t)$, defined on the extended phase space, defines a one-parameter group of canonical transformations which act on any function $f(q_{i}, t)$, in such a way that if $G$ is a constant of motion then from a solution of the Hamilton--Jacobi (HJ) equation one obtains a one-parameter family of solutions of the same HJ equation. It is also shown that any complete solution of the HJ equation can be obtained in this manner by means of the transformations generated by $n$ constants of motion in involution.

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Published

2014-01-01

How to Cite

[1]
G. Torres del Castillo, “Generation of solutions of the Hamilton--Jacobi equation”, Rev. Mex. Fís., vol. 60, no. 1 Jan-Feb, pp. 75–0, Jan. 2014.

Issue

Vol. 60 No. 1 Jan-Feb (2014): Revista Mexicana de Física.

Section

Articles

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.