67 citations · 524 across the 58 of their papers we have counts for
68 papers
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…
Towards the Erdős-Gallai Cycle Decomposition Conjecture
Matija Bucić, Richard Montgomery
In the 1960's, Erdős and Gallai conjectured that the edges of any -vertex graph can be decomposed into cycles and edges. We improve upon the previous best bound of $O(n\l…
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…