2019/10/31 by Alexander V Turbiner, Juan Carlos Lopez Vieyra · 1 citation
Physics and Astronomy · Mathematics · #physics.class-ph #hep-th #math-ph #math.DS #math.MP
paper · pdf · doi:10.1142/s0217732320501850
published as Mod Phys Lett A35 (2020) 2050185 · 4 pages, 1 figure, typos fixed, title modified, the correct value of elliptic modulus placed in p.2, left column
arxiv created 2020/04/22 · arxiv updated 2020/05/27
It is found explicitly 5 Liouville integrals in addition to total angular momentum which Poisson commute with Hamiltonian of 3-body Newtonian Gravity in \mathbb R3 along the Remarkable Figure-8-shape trajectory discovered by Moore-Chenciner-Montgomery. It is shown they become constants of motion along this trajectory. Hence, 3-body choreographic motion on Figure-8-shape trajectory in \mathbb R3 Newtonian gravity (Moore, 1993), as well as in \mathbb R2 modified Newtonian gravity by Fujiwara et al, 2003, is maximally superintegrable. It is conjectured that any 3-body potential theory which admit Figure-8-shape choreographic motion is superintegrable along the trajectory.