The scattering map in the planar restricted three body problem
We study homoclinic transport to Lyapunov orbits around a collinear libration point in the planar restricted three body problem. A method to compute homoclinic orbits is first described. Then we introduce the scattering map for this problem (defined on a suitable normally hyperbolic invariant manifold) and we show how to compute it using the information already obtained for the homoclinic orbits. An example application to Astrodynamics is also proposed.
KeywordsRestricted three body problem Homoclinic orbits Normally hyperbolic invariant manifolds Scattering map
Unable to display preview. Download preview PDF.
- Canalias, E., Masdemont, J.J.: Lunar space station for providing services to solar libration point missions. In 56th International Astronautical Federation Congress, Fukuoka, Japan (2005)Google Scholar
- Delshams, A., de la Llave, R., Seara, T.M.: A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model. Mem. Amer. Math. Soc. 179(844), 1–141 (2006)Google Scholar
- Farquhar, R.W.: A halo orbit lunar station. Astronautics and Aeronautics 10(6), 52–63 (1972)Google Scholar
- Gómez, G., Jorba, A., Masdemont, J.J., Simó, C.: A dynamical systems approach for the analysis of the SOHO mission. Third International Symposium on Spacecraft Flight Dynamics, ESA/ESOC, pp. 449–454, (1991)Google Scholar
- Robinson, C.: Dynamical systems. Studies in Advanced Mathematics 2nd edn. Stability, symbolic dynamics and chaos, CRS Press, Boca Raton (1999)Google Scholar
- Szebehely, V.: Theory of orbits. Academic Press, New York (1967)Google Scholar