Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. II. Mappings of first-order differential equations

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

DOI:https://doi.org/10.1063/1.526687· OSTI ID:6442779

Katzin, G H; Levine, J

Infinitesimal velocity-dependent symmetry mappings of second-order dynamical systems (a) E/sup i/(x, x, x, t)equivalentx/sup i/ -F/sup i/(x, x, t) = 0, i = 1,..., n, were studied in considerable detail in a previous paper (J. Math. Phys. 2X, xxxx (198X), the first of this series). Among the results developed in that paper was a procedure for determining the characteristic functional structure of symmetry mappings for such second-order systems. In this present companion paper it is shown that a similar procedure may be used to obtain the characteristic functional structure of infinitesimal symmetry mappings (b) y-bar/sup I/ = y/sup I/+deltay/sup I/, deltay/sup I/ equivalenteta/sup I/(y, t)deltaa; (c) t-bar = t+deltat, deltatequivalenteta/sup 0/(y, t)deltaa, for systems of first-order differential equations (d) E/sup I/(y, y, t)equivalenty/sup I/-lambda/sup I/ (y, t) = 0, I = 1,..., N. This characteristic structure is the same for all first-order systems (d) and is explicitly dependent upon constants of motion of the system.

• Research Organization: Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202
• OSTI ID: 6442779
• 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 & Mathematical Physics-- Relativity & 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