Symmetries and first integrals of some differential equations of dynamics

Journal Article · Mon Oct 01 00:00:00 EDT 1979 · Hadronic J.; (United States)

OSTI ID:6520040

Eliezer, C J

The theme of this paper is the study of the symmetry properties of some differential equations of dynamics, and of the construction of first integrals. For the time-dependent harmonic oscillator the Lewis invariant provides a quadratic function which is a constant of motion. Different derivatives are considered with a view to assigning some physical meaning to the invariant and to the function rho(t) in terms of which the invariant is expressed. Lie's theory of differential equations, which until recently has been sadly neglected in comparison with his other pioneering works, is applied to consider groups of point transformations which leave invariant the equations of motion. For the time-dependent oscillator, an eight-parameter Lie group is obtained. A five-parameter Noether sub-group leaves also the action function invariant. Some results concerning the symmetries of the Kepler problem are also reported. Dynamical symmetries, not covered by point transformations, are briefly discussed.

• Research Organization: La Trobe Univ., Victoria, Australia
• OSTI ID: 6520040
• Journal Information: Hadronic J.; (United States), Vol. 2:5
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HARMONIC OSCILLATORS
DIFFERENTIAL EQUATIONS
ANALYTICAL SOLUTION
CONSERVATION LAWS
DYNAMICS
INTEGRAL CALCULUS
LIE GROUPS
SYMMETRY
TIME DEPENDENCE
TRANSFORMATIONS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
MATHEMATICS
MECHANICS
OSCILLATORS
SYMMETRY GROUPS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics