LaplaceRungeLenz symmetry in general rotationally symmetric systems
Abstract
The universality of the LaplaceRungeLenz symmetry in all rotationally symmetric systems is discussed. The independence of the symmetry on the type of interaction is proven using only the most generic properties of the Poisson brackets. Generalized LaplaceRungeLenz vectors are definable to be constant (not only piecewise conserved) for all cases, including systems with open orbits. Applications are included for relativistic Coulomb systems and electromagnetic/gravitational systems in the postNewtonian approximation. The evidence for the relativistic origin of the symmetry are extended to all centrally symmetric systems.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 December 2010
 DOI:
 10.1063/1.3520521
 arXiv:
 arXiv:1005.1817
 Bibcode:
 2010JMP....51l2902B
 Keywords:

 Lorentz transformation;
 symmetry;
 03.30.+p;
 Special relativity;
 Mathematical Physics;
 Physics  Classical Physics;
 Physics  General Physics
 EPrint:
 doi:10.1063/1.3520521