SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS
Shang Meia, Mei Feng-xianga, Zhang Yib
a Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Basic Courses, Suzhou Institute of Urban Construction & Environmental Protection, Suzhou 215011, China
Abstract In this paper, the symmetries and the conserved quantities for systems of generalized classical mechanics are studied. First, the generalized Noether's theorem and the generalized Noether's inverse theorem of the systems are given, which are based upon the invariant properties of the canonical action with respect to the action of the infinitesimal transformation of r-parameter finite group of transformation; second, the Lie symmetries and conserved quantities of the systems are studied in accordance with the Lie's theory of the invariance of differential equations under the transformation of infinitesimal groups; and finally, the inner connection between the two kinds of symmetries of systems is discussed.
Received: 23 September 1999
Revised: 20 December 1999
Published: 12 June 2005