Dirac reduction of binary asteroid systems with symmetry and stability of relative equilibria

In this paper, we study symmetry reduction for a binary asteroid system modeled by a rigid body and a particle. In particular, we demonstrate how translational and rotational symmetry reduction appeared in the binary asteroid system can be carried out in the context of Dirac reduction by stages and with the associated reduction of implicit Hamiltonian systems. Then we investigate Stability of relative equilibria of the asteroid pair and show stability regions by using the energy-momentum method. Lastly, we illustrate some numerical simulations for stable and unstable orbits near from relative equilibria of the Collinear and T configurations.C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301311]

Analysis of equilibria in the doubly synchronous binary asteroid systems concerned with non-spherical shape

This paper investigates the equilibria and their stabilities in the doubly synchronous binary asteroid systems,which are modelled as the two tri-axial ellipsoids with various shape and system parameters.Particularly,the influences of shape and system parameters on equilibria are discussed analytically.Firstly,the geometrical models of doubly synchronous binary asteroid systems are established.The dual second degree and order gravity fleld is employed to approximate the gravitational potential of the system.Six shape and system parameters are deflned.Then,based on the linearized perturbation equations,the explicit expressions of the offsets of equilibria in doubly synchronous systems are derived,which clearly ilustrate the relationship between the distribution of equilibria and the variations of shape parameters.Further,the approximate expressions are applied to estimate the ftets of equilibria due to parameter etrors,respectively.Finally,in order to have a better insight into the equilibriaum structure,the sabiltis of equilibrisa under diferent system parameters are investigated.In particular,critical regions of triangular equilibria are calculated and the role of the relative distance on the stability is discussed in detail.This study could provide a preliminary analysis of equilibria for the mission design in doubly synchronous binary asteroid systems.

Forced motions around triangular libration points by solar radiation pressure in a binary asteroid system

By using two tri-axial ellipsoids to approximate the two asteroids,forced orbits around triangular libration points of the binary asteroid system(BAS)induced by solar radiation pressure are studied.The work is firstly carried out in the doubly synchronous binary asteroid system(DSBAS).The results show that the amplitude of the forced periodic orbit can be large,even for small to moderate surface area-to-mass ratios of the spacecraft.The position,amplitude,and stability of these forced periodic orbits are influenced by the asteroids'non-spherical terms.Also,the stability of them may be different,depending on the Sun's motion direction w.r.t.to the BAS's orbit motion direction.This study is then generalized to the asynchronous and synchronous BAS(ABAS and SBAS,respectively).The forced orbits in the complete system are quasi-periodic orbits around the forced periodic orbit of the averaged system.

A note on the full two-body problem and related restricted full three-body problem

Truncating at the second order of the mutual potential between two rigid bodies,time-explicit rst order solutions to the rotations and the orbital motion of the two bodies in the planar full two-body problem(F2BP)are constructed.Based on this analytical solution,equations of motion(EOMs)for the related restricted full three-body problem are given.In the case of the synchronous or double synchronous states for the full two-body problem,EOMs for the related restricted full three-body problem(RF3BP)are also given.At last,one example-the"collinear libration point"in the binary asteroid system-is given.