By Gerard Gomez, Angel Jorba, Josep J Masdemont
The purpose of this paintings is to provide an explanation for, examine and compute the types of motions that seem in a longer region of the geometrically outlined equilateral issues of the Earth-Moon method, as a resource of attainable nominal orbits for destiny area missions. The method built here's no longer particular to astrodynamics difficulties. The strategies are built in this sort of means that they are often used to review difficulties that may be modelled via dynamical structures.
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Additional resources for Dynamics and Mission Design Near Libration Points, Vol. IV: Advanced Methods for Triangular Points
With big fractal dimension) set of 2-dimensional tori in each level of energy. All these objects (periodic orbits and tori) are normally hyperbolic in their level of energy. It seems that the global stable manifold of this center manifold (WS(W£ )), which is a manifold of codimension 1, together with the corresponding unstable manifold (WU(W£ )), acts as the effective boundary of the stable set. It remains to compute this 5-dimensional manifold and intersect it with the set of the zero initial velocity.
We have also seen the role played by the fact that the orbit which replaces the libration point has a hyperbolic behavior in some directions. A transformation which (at least formally) skips the time dependence, if this is possible, produces an autonomous Hamiltonian again with a fixed point of saddle x center x center type instead of the points L4 or L5. Hence, these fixed points also have codimension 1 invariant manifolds. We suspect that the "stability" domains are confined by the codimension 1 manifolds (of center-stable and center-unstable type) associated to the periodic or quasi-periodic orbits which take the place of L3, L\ and L 5 .
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