Relative Motion Dynamics in the Restricted Three-Body Problem

2019 ◽  
Vol 56 (5) ◽  
pp. 1322-1337 ◽  
Author(s):  
Giovanni Franzini ◽  
Mario Innocenti
Keyword(s):  
Relative Motion ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body ◽  
Relative Motion Dynamics ◽  
Motion Dynamics

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.

On the modified circular restricted three-body problem with variable mass

New Astronomy ◽  
2021 ◽  
Vol 84 ◽  
pp. 101510
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Md Chand Asique ◽  
Amit Mittal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

2007 ◽  
Vol 17 (04) ◽  
pp. 1151-1169 ◽  
Author(s):  
MARIAN GIDEA ◽  
JOSEP J. MASDEMONT
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Invariant Manifolds ◽  
Libration Point ◽  
Homoclinic Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lyapunov Orbits ◽  
Homoclinic Connections ◽  
Three Body

The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

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