Lie and Lie-admissible symmetries of dynamical systems

Conference · Sat Dec 01 04:00:00 EST 1979 · Hadronic J.; (United States)

OSTI ID:6759008

Prince, G E ^[1]; Leach, P G.L.; Kalotas, T M; Eliezer, C J; Santilli, R M

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1. 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-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 3:1
• Country of Publication: United States
• Language: English

Related Subjects

657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
HAMILTON-JACOBI EQUATIONS
LIE GROUPS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE-TIME
SYMMETRY
SYMMETRY GROUPS
TRANSFORMATIONS