On the Symmetries of the Manev Problem and Its Real Hamiltonian Form

Abstract

The Manev model and its real form dynamics are known to possess Ermanno–Bernoulli type invariants similar to the Laplace–Runge–Lenz vector of the Kepler model. Using these additional invariants, we demon- strate here that both Manev model and its real Hamiltonian form posses the same $\mathfrak{so}(3)$ or $\mathfrak{so}(2,1)$ symmetry algebras (in addition to the angular momentum algebra) on angular momentum level sets. Thus Kepler and Manev models are shown to have identical symmetry algebras and hence sharing more features than previously expected.