Periodic solutions of a galactic potential

New families of periodic orbits for a galactic potential

“…We remark that the periodic orbits corresponding to the families V, VI and VII found in [9] are rectilinear or circular.…”

“…Here we improve the results of [9] finding new families of periodic orbits, also using a result based in the averaging theory. The key point for obtaining these new families of periodic orbits is to work with the Lissajous variables instead of working directly with the cartesian variables (Q 1 , Q 2 , Q 3 , P 1 , P 2 , P 3 ) as in [9].…”

“…From Table 1 is easily to obtain the implicit equations of two of the periodic orbits of the family I for ε = 0, which are given by the intersection of the elliptic cylinder We must mention that in the paper [9] three more additional families of periodic orbits of the Hamiltonian system defined by the Hamiltonian (3) with the perturbation given by (2) were found in our notation they are:…”

“…In the paper of [9] the authors studied analytically the families of periodic orbits of the Hamiltonian (1) with (2) using the averaging theory, and they find several families of periodic orbits. Here we improve the results of [9] finding new families of periodic orbits, also using a result based in the averaging theory.…”

“…In this case, we obtain the following solutions (G 0 , g 0 , N 0 , n 0 ) satisfying (7) For I, II and III the value of the Jacobian ∆ is a 2 (a − 2) 2 (a 2 − 36)L 4 (18 − a) 3 and is not zero for a = −6 and 6. For β = 0 there are also the solutions (V) and (VI) already studied in [9].…”