P. Tibboel

activity

20112022

most citedExistence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous

n

-body problems and the curved

n

-body problem

8 citations · 11 across the 13 of their papers we have counts for

collaborators

16 papers

math.CA2022

A proof of Saari's homographic conjecture

Pieter Tibboel

We prove Saari's homographic conjecture for a large class of $n$ -body problems with power law potentials, including the classical $n$ -body problem.

math.CA2022

A proof of Saari's conjecture

Pieter Tibboel

We prove Saari's conjecture, which states that for any solution to the classical $n$ -body problem that has constant (polar) moment of inertia has to behave as a rotating rigid body…

math.CA2020

Classification of positive elliptic-elliptic rotopulsators on Clifford tori

Pieter Tibboel

We prove that positive elliptic-elliptic rotopulsator solutions of the $n$ -body problem in spaces of constant Gaussian curvature that move on Clifford tori of nonconstant size eith…

math.CA2020

Positive elliptic-elliptic rotopulsators on Clifford tori of nonconstant size project onto regular polygons

Pieter Tibboel

Let $q_{1}$ ,..., $q_{n}$ be the position vectors of the point masses of the curved $n$ -body problem. Consider any positive elliptic-elliptic rotopulsator solution $q_{i}^{T}=(r\cos{…

math.CA2020

Equal masses results for choreographies $n$ -body problems

Pieter Tibboel

We prove that equally spaced choreography solutions of a large class of $n$ -body problems including the classical $n$ -body problem and a subset of quasi-homogeneous $n$ -body proble…

math-ph2018

Circular non-collision orbits for a large class of n-body problems

Pieter Tibboel

We prove for a large class of n-body problems including a subclass of quasihomogeneous n-body problems, the classical n-body problem, the n-body problem in spaces of negative const…

math.DS2018★ 3 cited

Polygonal rotopulsators of the curved $n$ -body problem

Pieter Tibboel

We revisit polygonal positive elliptic rotopulsator solutions and polygonal negative elliptic rotopulsator solutions of the $n$ -body problem in $H^{3}$ and $\mathbb{S}^{3}…

math.DS2016

Polygonal negative hyperbolic rotopulsators of the curved $n$ -body problem

Pieter Tibboel

For the $n$ -body problem in spaces of negative constant Gaussian curvature, we prove for a class of negative hyperbolic rotopulsators that if that class exists, the configurations…

math-ph2016

Finiteness of polygonal relative equilibria for generalised quasi-homogeneous $n$ -body problems and $n$ -body problems in spaces of constant curvature

Pieter Tibboel

We prove for generalisations of quasi-homogeneous $n$ -body problems with center of mass zero and $n$ -body problems in spaces of negative constant Gaussian curvature that if the mas…

math.DS2015★ 8 cited

Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous $n$ -body problems and the curved $n$ -body problem

Pieter Tibboel

We prove that if for relative equilibrium solutions of a generalisation of quasi-homogeneous $n$ -body problems the masses and rotation are given, then the minimum distance between…

math.DS2014

Existence of a lower bound for the distance between point masses of relative equilibria in $S^{k - 1}$ , $k \geq 3$

Pieter Tibboel

We prove that if for the curved $n$ -body problem in $S^{k - 1}$ , $k \geq 3$ , the masses are given, the minimum distance between the point masses of a specific type of relativ…

math.DS2014

On the minimum distance between masses of relative equilibria of the $n$ -body problem

Pieter Tibboel

We prove that if for relative equilibrium solutions of a generalisation of the $n$ -body problem of celestial mechanics the masses and rotation are given, then the minimum distance…

math.DS2014

Existence of a lower bound for the distance between point masses of relative equilibria in spaces of constant curvature

Pieter Tibboel

We prove that if for the curved $n$ -body problem the masses are given, the minimum distance between the point masses of a specific type of relative equilibrium solution to that pro…

math.DS2013

Finiteness of classes of relative equilibria for the $n$ -body problem

Pieter Tibboel

We prove that if the masses of the $n$ -body problem of celestial mechanics are given, the number of classes of relative equilibria that solve the $n$ -body problem is finite.

math.DS2012

Existence of a class of rotopulsators

Pieter Tibboel

We prove the existence of a class of rotopulsators for the n-body problem in spaces of constant curvature of dimension k>=2.

math.DS2011

Polygonal homographic orbits in spaces of constant curvature

Pieter Tibboel

We prove that the geometry of the 2-dimensional $n$ -body problem for spaces of constant curvature $κ \neq = 0$ , $n \geq 3$ , does not allow for polygonal homographic solutions, provided…

A proof of Saari's homographic conjecture

A proof of Saari's conjecture

Classification of positive elliptic-elliptic rotopulsators on Clifford tori

Positive elliptic-elliptic rotopulsators on Clifford tori of nonconstant size project onto regular polygons

Equal masses results for choreographies n-body problems

Circular non-collision orbits for a large class of n-body problems

Polygonal rotopulsators of the curved n-body problem

Polygonal negative hyperbolic rotopulsators of the curved n-body problem

Finiteness of polygonal relative equilibria for generalised quasi-homogeneous n-body problems and n-body problems in spaces of constant curvature

Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous n-body problems and the curved n-body problem

Existence of a lower bound for the distance between point masses of relative equilibria in Sk−1, k≥3

On the minimum distance between masses of relative equilibria of the n-body problem

Existence of a lower bound for the distance between point masses of relative equilibria in spaces of constant curvature

Finiteness of classes of relative equilibria for the n-body problem

Existence of a class of rotopulsators

Polygonal homographic orbits in spaces of constant curvature

Equal masses results for choreographies $n$ -body problems

Polygonal rotopulsators of the curved $n$ -body problem

Polygonal negative hyperbolic rotopulsators of the curved $n$ -body problem

Finiteness of polygonal relative equilibria for generalised quasi-homogeneous $n$ -body problems and $n$ -body problems in spaces of constant curvature

Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous $n$ -body problems and the curved $n$ -body problem

Existence of a lower bound for the distance between point masses of relative equilibria in $S^{k - 1}$ , $k \geq 3$

On the minimum distance between masses of relative equilibria of the $n$ -body problem

Finiteness of classes of relative equilibria for the $n$ -body problem