Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. II. Mappings of first-order differential equations
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), Vol. 26:12
- Country of Publication:
- United States
- Language:
- English
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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