Fradkin-Bacry-Ruegg-Souriau perihelion vector for Gorringe-Leach equations

Abstract

We show that every generalized Gorringe-Leach equation admits an associated Fradkin-Bacry-Ruegg-Souriau's vector which, in general, is only a piecewise conserved quantity. In the case of dualizable generalized Gorringe-Leach equations, which include the case of conservative motions in central power law potentials, the image sets of the FBRS vectors for dual classes are dual images of each other.

Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time

“…The construction of FBRS vector can be readily done by re-expressing the central force problem in the complex plane [13]. We briefly summarise the essential steps of re-expressing the central potential problem in the complex plane.…”

“…The existence of a conserved vector, FBRS vector, for a central potentials natually lead to attempts to construct similar conserved quantities for dissipative systems also. The idea that dissipative system can be mapped to a system with no drag term is well known in the commutative case [13]. This method have been used to obtian a conserved vector for dissipative systems.…”

“…This method have been used to obtian a conserved vector for dissipative systems. In this section, we generalize the procedure of [13] by Grandati et.al. on Gorringe-Leach equation to the kappa-deformed space-time and establishes the existence of a piecewise conserved quantity.…”

“…It was shown by Grandati et al [13] that every generalized Gorringe-Leach equation admits an asso-ciated FBRS vector which is globally conserved for the equations of a particular class. For the dualizable generalized Gorringe-Leach equations, Grandati et al [13] showed the image sets of the discontinuous FBRS vectors for two classes of power potential problems are dual images of each other. In this paper we study the non-commutative generalization of the Gorringe-Leach equations in the κ-space time also.…”