Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. I. Velocity-dependent mappings of second-order differential equations
The primary purpose of this paper is to show that infinitesimal velocity-dependent symmetry mappings ((a) x-bar/sup i/ = x/sup i/ +deltax/sup i/, deltax/sup i/ equivalent xi/sup i/(x,x,t)deltaa with associated change in path parameter (b) t-bar = t+deltat, deltat equivalent xi/sup 0/(x,x,t)) of classical (including relativistic) particle systems (c) E/sup i/(x,x,x,t) = 0 are expressible in a form with a characteristic functional structure which is the same for all dynamical systems (c) and is manifestly dependent upon constants of motion of the system. In this characteristic form the symmetry mappings are determined by (d) xi/sup i/ = Z/sup i/(x,x,t) +x/sup i/xi/sup 0/,xi/sup 0/ arbitrary; the functions Z/sup i/ appearing in (d) have the form (e) Z/sup i/ = B/sup A/g/sup i//sub A/(C/sup 1/,...,C/sup r/; t), 0< or =r< or =2n, A = 1,...,2n, where the B/sup A/ are arbitrary constants of motion and the C's appearing in the functions g/sup i//sub A/ are specified constants of motion.
- Research Organization:
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202
- OSTI ID:
- 6333660
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Vol. 26:12
- Country of Publication:
- United States
- Language:
- English
Similar Records
Energy--momentum tensor symmetries and concomitant conservation laws. I. Einstein-massless-scalar (meson) field
Quantum effects on the vacuum symmetries of gauge supersymmetry
Related Subjects
GENERAL PHYSICS
GENERAL RELATIVITY THEORY
SYMMETRY
TOPOLOGICAL MAPPING
PARTIAL DIFFERENTIAL EQUATIONS
ANALYTICAL SOLUTION
DYNAMICS
RELATIVITY THEORY
VELOCITY
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
MAPPING
MECHANICS
TRANSFORMATIONS
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation