E Barrabés et al 2009 Nonlinearity 22 2901 doi:10.1088/0951-7715/22/12/006
E Barrabés1, J M Mondelo2 and M Ollé3
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The goal of this paper is the numerical computation and continuation of homoclinic connections of the Lyapunov families of periodic orbits (p.o.) associated with the collinear equilibrium points, L1, L2 and L3, of the planar circular restricted three-body problem (RTBP). We describe the method used that allows us to follow individual families of homoclinic connections by numerical continuation of a system of (nonlinear) equations that has as unknowns the initial condition of the p.o., the linear approximation of its stable and unstable manifolds and a point in a given Poincaré section in which the unstable and stable manifolds match. For the L3 case, some comments are made on the geometry of the manifold tubes and the possibility of obtaining trajectories with prescribed itineraries.
45.50.Jf Few- and many-body systems
95.10.Eg Orbit determination and improvement
02.60.Jh Numerical differentiation and integration
70K44 Homoclinic and heteroclinic trajectories
Issue 12 (December 2009)
Received 26 January 2009, in final form 6 October 2009
Published 30 October 2009
E Barrabés et al 2009 Nonlinearity 22 2901
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