On relative equilibria of mutually gravitating massive point and triangular rigid body

Abstract

AbstractPlanar motions of a triangular body and a massive point under the action of mutual Newtonian attraction are studied. For the first formulation the triangle is assumed to be composed of three massive points. For the second formulation it is constructed with three homogeneous rods. Some partial solutions are observed within the analysis of the geometry of mass distribution.The investigation is motivated by the problem of motion of spacecrafts near asteroid-like celestial objects possessing irregular mass distribution. Comparison of dynamical effects for two types of mass distribution is another goal of the research.Problems appearing because of irregularities in mass distributions have been known for a long time. Certain approaches to the description of motions under attraction as well as qualitative particulars of dynamics are discussed by Demin (1963), Burov & Karapetyan (1995), Buchin & Burov & Troger (2008), Burov & Guerman & Sulikashvili (2010), Kholshevnikov & Kuznetsov (2011), Beletsky & Rodnikov (2011) and Scheeres (2012).