The planar restricted three-body problem when both primaries are triaxial rigid bodies: Equilibrium points and periodic orbits

2016 ◽  
Vol 361 (9) ◽  
Author(s):  
S. M. Elshaboury ◽  
Elbaz I. Abouelmagd ◽  
V. S. Kalantonis ◽  
E. A. Perdios
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Equilibrium Points ◽  
Rigid Bodies ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

Motion around the Triangular Equilibrium Points in the Circular Restricted Three-Body Problem under Triaxial Luminous Primaries with Poynting-Robertson Drag

2017 ◽  
Vol 12 ◽  
pp. 1-21
Author(s):  
Jagadish Singh ◽  
Ayas Mungu Simeon
Keyword(s):  
Linear Stability ◽  
Binary Stars ◽  
Body Problem ◽  
Equilibrium Points ◽  
Rigid Bodies ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Numerical Application ◽  
Triangular Points ◽  
Three Body

This paper explores the motion of an infinitesimal body around the triangular equilibrium points in the framework of circular restricted three-body problem (CR3BP) with the postulation that the primaries are triaxial rigid bodies, radiating in nature and are also under the influence of Poynting–Robertson (P-R) drag. We study the linear stability of these triangular points and for the numerical application, the binary stars Kruger 60 (AB) and Archird have been considered. These triangular points are not only perceived to move towards the line joining the primaries in the direction of the bigger primary with increasing triaxiality, they are also unstable owing to the destabilizing influence of P-R drag.

scholarly journals Semianalytical Solutions of Relative Motions with Applications to Periodic Orbits about a Nominal Circular Orbit

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Qiwei Guo ◽  
Hanlun Lei ◽  
Bo Xu
Keyword(s):  
Periodic Orbits ◽  
Relative Motion ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
State Variables ◽  
Three Body Problem ◽  
Reference Orbit ◽  
Three Body ◽  
Modal Coordinates

In the dynamical model of relative motion with circular reference orbit, the equilibrium points are distributed on the circle where the leader spacecraft is located. In this work, analytical solutions of periodic configurations around an arbitrary equilibrium point are constructed by taking Lindstedt-Poincaré (L-P) and polynomial expansion methods. Based on L-P approach, periodic motions are expanded as formal series of in-plane and out-of-plane amplitudes. According to the method of polynomial expansions, a pair of modal coordinates is chosen, and the remaining state variables are expressed as polynomial series about the modal coordinates. In order to check the validity of series solutions constructed, the practical convergence is evaluated. Considering the fact that relative motion model is a special case of restricted three-body problem, the periodic configurations constructed in the model of relative motion are taken as starting solutions to numerically identify the periodic orbits in restricted three-body problem by means of continuation technique with the mass of system as continuation parameter.

Sign in / Sign up

Export Citation Format

Share Document