Lie and Lie-admissible symmetries of dynamical systems
- La Trobe Univ., Victoria, Australia
In this paper we recall Lie's method for the construction of the generators of Lie symmetry groups from given second-order equations of motion, and provide an illustrative example. The method is then adapted to the equations of motion in their equivalent first-order (vector field) form, and an example is discussed in terms of Hamilton's equations. The first-order version of Lie's method is then studied for the construction of Lie-admissible symmetry groups, that is, connected Lie groups realized in such a way to admit a non-Lie, but Lie-admissible lgebra in the neighborhood of the identity, as a nonconservative extension of the conventional Lie description of conservative mechanics. Some problems of using Lie's method for the construction of a Lie-admissible symmetry when the transformation includes a coordinate-dependent time change are discussed.
- DOE Contract Number:
- AC02-78ER04742
- OSTI ID:
- 6759008
- Report Number(s):
- CONF-7908175-
- Journal Information:
- Hadronic J.; (United States), Vol. 3:1; Conference: 2. workshop on Lie-admissible formulations, Cambridge, MA, USA, 1 Aug 1979
- Country of Publication:
- United States
- Language:
- English
Similar Records
Possible Lie-admissible covering of the Galilei relativity in Newtonian mechanics for nonconservative and Galilei form-noninvariant systems
Initiation of the representation theory of Lie-admissible algebras of operators on bimodular Hilbert spaces
Related Subjects
GENERAL PHYSICS
HAMILTON-JACOBI EQUATIONS
LIE GROUPS
EQUATIONS OF MOTION
CONSERVATION LAWS
SPACE-TIME
SYMMETRY
TRANSFORMATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY GROUPS
658000* - Mathematical Physics- (-1987)
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics