Generation of solutions of the Hamilton-Jacobi equation
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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Sociedad Mexicana de Física
2014
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oai:scielo:S0035-001X20140001000122014-03-26Generation of solutions of the Hamilton-Jacobi equationTorres del Castillo,G. F. Hamilton-Jacobi equation canonical transformations constants of motion 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.info:eu-repo/semantics/openAccessSociedad Mexicana de FísicaRevista mexicana de física v.60 n.1 20142014-02-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0035-001X2014000100012en |
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México |
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MX |
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revista |
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America del Norte |
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| language |
English |
| format |
Digital |
| author |
Torres del Castillo,G. F. |
| spellingShingle |
Torres del Castillo,G. F. Generation of solutions of the Hamilton-Jacobi equation |
| author_facet |
Torres del Castillo,G. F. |
| author_sort |
Torres del Castillo,G. F. |
| title |
Generation of solutions of the Hamilton-Jacobi equation |
| title_short |
Generation of solutions of the Hamilton-Jacobi equation |
| title_full |
Generation of solutions of the Hamilton-Jacobi equation |
| title_fullStr |
Generation of solutions of the Hamilton-Jacobi equation |
| title_full_unstemmed |
Generation of solutions of the Hamilton-Jacobi equation |
| title_sort |
generation of solutions of the hamilton-jacobi equation |
| description |
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. |
| publisher |
Sociedad Mexicana de Física |
| publishDate |
2014 |
| url |
http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0035-001X2014000100012 |
| work_keys_str_mv |
AT torresdelcastillogf generationofsolutionsofthehamiltonjacobiequation |
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