67 citations · 524 across the 58 of their papers we have counts for
25 papers · 1 filter
Approach to total collision in the spatial 4-body problem
Richard Montgomery, Guowei Yu
Every solution for the classical four body problem in space which ends in total collision has a limiting shape. We prove that when that shape is planar the entire solution lies in…
Halfway between Heaven and Hell
Richard Montgomery
We pose several questions for the classical N-body problem inspired by connections between the virial equation and the Jacobi-Maupertuis formulationof mechanics. We answer some.
Compactification of the energy surfaces for n bodies
Andreas Knauf, Richard Montgomery
For n bodies moving in Euclidean d-space under the influence of a homogeneous pair interaction we compactify every center-of-mass energy surface, obtaining a 2d(n -1)-1 - dimension…
No Infinite Spin for Planar Total Collision
Richard Moeckel, Richard Montgomery
The infinite spin problem concerns the rotational behavior of total collision orbits in the -body problem. It has long been known that when a solution tends to total collision t…
Dropping Bodies
Richard Montgomery
The subject is brake orbits for the 3-body problem: orbits where all velocities are zero at some instant. We extract a paradox and a mystery out of a recent database of 30 non-coll…
Classical -body scattering with long-range potentials
Jacques Féjoz, Andreas Knauf, Richard Montgomery
We consider the scattering of classical particles interacting via pair potentials, under the assumption that each pair potential is "long-range", i.e. being of order ${\cal O}(…