This article is cited in 1 paper

Special Issue: On the 80th birthday of professor A. Chenciner

Brake Orbits Fill the N-Body Hill Region

Richard Montgomery

Dept. of Mathematics, UCSC, 1156 High Street, 95064 Santa Cruz, CA

Abstract: 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.

MSC: 37J50, 70H99

Received: 30.11.2022
Accepted: 21.04.2023

Language: English

DOI: 10.1134/S1560354723520027