FIRST INTEGRALS ASSOCIATED WITH THE ADDITIONAL SYMMETRY OF CENTRAL FORCE PROBLEMS WITH POWER LAW POTENTIALS

Abstract

It has recently been shown by Leach and Gorringe that the equation of motion is invariant under the action of the symmetry G = t ∂/∂t + αr ∂/∂r in addition to the usual time and rotation symmetries in contrast to the occurrence of two extra symmetries for the charge monopole problem (Moreira et al, J Phys, 18 (1985) L427). The integrals associated with G are calculated and an interesting connection with Hamilton-Jacobi theory demonstrated.