# Spatial collinear restricted four-body problem with repulsive Manev potential

Spatial collinear restricted four-body problem with repulsive Manev potential We outline some aspects of the dynamics of an infinitesimal mass under the Newtonian attraction of three point masses in a symmetric collinear relative equilibria configuration when a repulsive Manev potential ( $$-1/r +e/r^{2}$$ - 1 / r + e / r 2 ), $$e>0$$ e > 0 , is applied to the central mass. We investigate the relative equilibria of the infinitesimal mass and their linear stability as a function of the mass parameter $$\beta$$ β , the ratio of mass of the central body to the mass of one of two remaining bodies, and e. We also prove the nonexistence of binary collisions between the central body and the infinitesimal mass. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Celestial Mechanics and Dynamical Astronomy Springer Journals

# Spatial collinear restricted four-body problem with repulsive Manev potential

, Volume 129 (2) – Jun 20, 2017
24 pages

/lp/springer_journal/spatial-collinear-restricted-four-body-problem-with-repulsive-manev-cD3F0qm0R0
Publisher
Springer Netherlands
Subject
Physics; Astrophysics and Astroparticles; Dynamical Systems and Ergodic Theory; Aerospace Technology and Astronautics; Geophysics/Geodesy; Classical Mechanics
ISSN
0923-2958
eISSN
1572-9478
D.O.I.
10.1007/s10569-017-9771-y
Publisher site
See Article on Publisher Site

### Abstract

We outline some aspects of the dynamics of an infinitesimal mass under the Newtonian attraction of three point masses in a symmetric collinear relative equilibria configuration when a repulsive Manev potential ( $$-1/r +e/r^{2}$$ - 1 / r + e / r 2 ), $$e>0$$ e > 0 , is applied to the central mass. We investigate the relative equilibria of the infinitesimal mass and their linear stability as a function of the mass parameter $$\beta$$ β , the ratio of mass of the central body to the mass of one of two remaining bodies, and e. We also prove the nonexistence of binary collisions between the central body and the infinitesimal mass.

### Journal

Celestial Mechanics and Dynamical AstronomySpringer Journals

Published: Jun 20, 2017

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