8 citations · 11 across the 13 of their papers we have counts for
5 papers · 1 filter
A proof of Saari's homographic conjecture
Pieter Tibboel
We prove Saari's homographic conjecture for a large class of -body problems with power law potentials, including the classical -body problem.
A proof of Saari's conjecture
Pieter Tibboel
We prove Saari's conjecture, which states that for any solution to the classical -body problem that has constant (polar) moment of inertia has to behave as a rotating rigid body…
Classification of positive elliptic-elliptic rotopulsators on Clifford tori
Pieter Tibboel
We prove that positive elliptic-elliptic rotopulsator solutions of the -body problem in spaces of constant Gaussian curvature that move on Clifford tori of nonconstant size eith…
Positive elliptic-elliptic rotopulsators on Clifford tori of nonconstant size project onto regular polygons
Pieter Tibboel
Let ,..., be the position vectors of the point masses of the curved -body problem. Consider any positive elliptic-elliptic rotopulsator solution $q_{i}^{T}=(r\cos{…
Equal masses results for choreographies -body problems
Pieter Tibboel
We prove that equally spaced choreography solutions of a large class of -body problems including the classical -body problem and a subset of quasi-homogeneous -body proble…