Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. I. Velocity-dependent mappings of second-order differential equations

Journal Article · Sun Dec 01 04:00:00 EST 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526686· OSTI ID:6333660

Katzin, G H; Levine, J

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), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:12; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical &amp; Mathematical Physics-- Relativity &amp; Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
DYNAMICS
EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
MAPPING
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
RELATIVITY THEORY
SYMMETRY
TOPOLOGICAL MAPPING
TRANSFORMATIONS
VELOCITY