Open AccessA conservation theorem of Hojman for systems of generalized classical mechanics
Author(s) -
Yi Zhang
Publication year - 2003
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.52.1832
Subject(s) - conservation law , infinitesimal , generalization , homogeneous space , analytical mechanics , ordinary differential equation , mathematical physics , space (punctuation) , conserved quantity , mathematics , classical mechanics , physics , pure mathematics , differential equation , mathematical analysis , quantum mechanics , computer science , quantum statistical mechanics , geometry , quantum , operating system
The conservation theorem and the symmetries for systems of generalized classical mechanics are studied. In terms of the invariance of the ordinary differential equations under the infinitesimal transformations, this paper established the Li e symmetrical transformations of the systems in the high-dimensional extended ph ase space, which only depend on the canonical variables, and a new type of conse rvation laws are directly obtained from the Lie symmetries of the systems. Actua lly, the conservation laws are the generalization of a conservation theorem of H ojman to generalized classical mechanics. Finally, an example is given to illust rate the application of the results.