TY - JOUR

T1 - Circular Non-collision Orbits for a Large Class of n-Body Problems

AU - Tibboel, Pieter

N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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 constant Gaussian curvature and a restricted case of the n-body problem in spaces of positive constant curvature for the case that all masses are equal and not necessarily constant that any solution for which the point masses move on a circle of not necessarily constant size has to be either a regular cocircular homographic orbit in flat space, or a regular polygonal rotopulsator in curved space, under the constraint that the minimal distance between point masses attains its minimum in finite time. Additionally, we prove that the same holds true if we add an extra mass at the center of that circle and find an explicit formula for the mass of each point particle in terms of the radius of the circle. Finally, we prove that for each order of the masses there is at most one cocircular homographic orbit for the case that the masses need not be constant.

AB - 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 constant Gaussian curvature and a restricted case of the n-body problem in spaces of positive constant curvature for the case that all masses are equal and not necessarily constant that any solution for which the point masses move on a circle of not necessarily constant size has to be either a regular cocircular homographic orbit in flat space, or a regular polygonal rotopulsator in curved space, under the constraint that the minimal distance between point masses attains its minimum in finite time. Additionally, we prove that the same holds true if we add an extra mass at the center of that circle and find an explicit formula for the mass of each point particle in terms of the radius of the circle. Finally, we prove that for each order of the masses there is at most one cocircular homographic orbit for the case that the masses need not be constant.

KW - Celestial mechanics

KW - Curved n-body problem

KW - Homographic orbits

KW - Rotopulsators

KW - n-body problems

UR - http://www.scopus.com/inward/record.url?scp=85055991334&partnerID=8YFLogxK

U2 - 10.1007/s10884-018-9714-7

DO - 10.1007/s10884-018-9714-7

M3 - Article

AN - SCOPUS:85055991334

SN - 1040-7294

VL - 32

SP - 205

EP - 217

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 1

ER -