# 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:

- (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}

}