Abstract
Regions of possible motions are established for dynamical systems possessing time-independent Hamiltonians or for systems which are reducible to that form by means of integrals of the motion using only extended point transformations. The method is applied to the problem of three bodies in a plane and surfaces of zero velocity are found. The governing parameters are the energy, angular momentum and the masses of the participating bodies. The analytical and geometrical properties of these surfaces provide qualitative results for given constants of the motion.
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Zare, K. The effects of integrals on the totality of solutions of dynamical systems. Celestial Mechanics 14, 73–83 (1976). https://doi.org/10.1007/BF01247133
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DOI: https://doi.org/10.1007/BF01247133