Open AccessTHE TRANSFORMATION PROPERTIES OF CONSTRAINED SYSTEM
Author(s) -
Ziping Li
Publication year - 1981
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.30.1659
Subject(s) - noether's theorem , transformation (genetics) , infinitesimal , infinitesimal transformation , conservation law , invariant (physics) , equations of motion , constraint (computer aided design) , mathematics , mathematical analysis , classical mechanics , physics , mathematical physics , lagrangian , biochemistry , chemistry , geometry , gene
The motion of constrained system may be described in terms of non-independent state functions. We considered the change of the action integral and constraint equations under the infinitesimal transformation of the time-space points and state functions of the constrained system, this leads to the general transformation result. We obtained the general equations for the transformation properties of constrained system along the trajectory of motion of that system. From these equations, the condition under which the transformation of constrained system yields conservation law can be worked out. For some specific transformations of the continuous system, we have found the equations of transformation properties. In the special cases, the general equations of transformation properties can be reduced to the results the classical Noether's theorem, The application of general results to classical mechanics is discussed in detail and the Poincare-Cartan invariant is generalized to the constrained system.