Richard Moeckel

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math.DS2026

Orbits of the three-body problem with large potential

Richard Moeckel

Consider the planar three-body problem with masses positive $m_{1}, m_{2}, m_{3}$ position vector $q (t) = (q_{1} (t), q_{2} (t), q_{3} (t)) \in R^{6}$ . Let $$U(q) = \frac{m_1m_2}{r_{12}}+\frac{m…

math.DS2026

Scattering in the Positive Energy Isosceles Three-Body Problem

Richard Moeckel

In the three-body problem with positive energy, solutions which avoid triple collision have the property that the size of the triangle formed by the bodies tends to infinity as $t\…

math.DS2025

Partially rigid motions in the planar three-body problem

Richard Moeckel

A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion.…