2023/07/26 by Hounkonnou, Mahouton Norbert, Landalidji, Mahougnon Justin
#(2010): 37C10 #37J35 #37K05 #37K10 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2308.08450
The problem of Kepler dynamics on a conformable Poisson manifold is addressed. The Hamiltonian function is defined and the related Hamiltonian vector field governing the dynamics is derived, which leads to a modified Newton second law. Conformable momentum and Laplace-Runge-Lenz vectors are considered, generating SO(3), SO(4), and SO(1, 3) dynamical symmetry groups. The corresponding first Casimir operators of SO(4) and SO(1, 3) are, respectively, obtained. The recursion operators are constructed and used to compute the integrals of motion in action-angle coordinates. Main relevant properties are deducted and discussed.