Brake Orbits Fill the N-body Hill Region

    2023, Volume 28, Numbers 4-5, pp.  374-394

    Author(s): Montgomery R.

    A brake orbit for the N-body problem is a solution for which, at some instant, all velocities of all bodies are zero. We reprove two “lost theorems” regarding brake orbits and use them to establish some surprising properties of the completion of the Jacobi – Maupertuis metric for the N-body problem at negative energies.
    Keywords: N-body problem, Hill region, Jacobi – Maupertuis metric, brake orbit, zero velocity surface
    Citation: Montgomery R., Brake Orbits Fill the N-body Hill Region, Regular and Chaotic Dynamics, 2023, Volume 28, Numbers 4-5, pp. 374-394
    DOI: 10.1134/S1560354723520027



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