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Title: Lie and Lie-admissible symmetries of dynamical systems

Abstract

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.

Authors:
 [1]; ; ; ;
  1. (La Trobe Univ., Victoria, Australia)
Publication Date:
OSTI Identifier:
6759008
Alternate Identifier(s):
OSTI ID: 6759008
Report Number(s):
CONF-7908175-
Journal ID: CODEN: HAJOD
DOE Contract Number:  
AC02-78ER04742
Resource Type:
Conference
Resource Relation:
Journal Name: Hadronic J.; (United States); Journal Volume: 3:1; Conference: 2. workshop on Lie-admissible formulations, Cambridge, MA, USA, 1 Aug 1979
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, 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

Citation Formats

Prince, G.E., Leach, P.G.L., Kalotas, T.M., Eliezer, C.J., and Santilli, R.M... Lie and Lie-admissible symmetries of dynamical systems. United States: N. p., 1979. Web.
Prince, G.E., Leach, P.G.L., Kalotas, T.M., Eliezer, C.J., & Santilli, R.M... Lie and Lie-admissible symmetries of dynamical systems. United States.
Prince, G.E., Leach, P.G.L., Kalotas, T.M., Eliezer, C.J., and Santilli, R.M... Sat . "Lie and Lie-admissible symmetries of dynamical systems". United States. doi:.
@article{osti_6759008,
title = {Lie and Lie-admissible symmetries of dynamical systems},
author = {Prince, G.E. and Leach, P.G.L. and Kalotas, T.M. and Eliezer, C.J. and Santilli, R.M..},
abstractNote = {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.},
doi = {},
journal = {Hadronic J.; (United States)},
number = ,
volume = 3:1,
place = {United States},
year = {Sat Dec 01 00:00:00 EST 1979},
month = {Sat Dec 01 00:00:00 EST 1979}
}

Conference:
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