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physics.class-ph2021★ 4 cited
Superintegrability of -body choreographies, on the algebraic Lemniscate by Bernoulli (inverse problem of classical mechanics)
Alexander V. Turbiner, Juan Carlos Lopez Vieyra
For one 3-body and two 5-body planar choreographies on the same algebraic Lemniscate by Bernoulli we found explicitly a maximal possible set of (particular) Liouville integrals, 7…
physics.class-ph2019★ 5 cited
Particular superintegrability of 3-body (modified) Newtonian Gravity
Alexander V Turbiner, Juan Carlos Lopez Vieyra
It is found explicitly 5 Liouville integrals in addition to total angular momentum which Poisson commute with Hamiltonian of 3-body Newtonian Gravity in along the R…