Geometric numerical propagation of redundant orbital problems

• Autores: Manuel Pedro Palacios Latasa
• Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques / coord. por Manuel Pedro Palacios Latasa , David Trujillo, Juan José Torrens Iñigo , Monique Madaune-Tort , María Cruz López de Silanes Busto , Gerardo Sanz Sáiz , 2003, ISBN 84-7733-720-9, págs. 209-217
• Idioma: inglés
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• Resumen

  • In order to increase the efficiency in the numerical integration of orbital problems it is need, firstly, the formulation of the problem in the adequate set of variables. It has been revealed that the formulation in regularized projective variables referred to the ideal frame is very adequate. The difficulty of this formulation is based on the existence of constrains, which, traditionally, have been used as control for the progress of the numerical calculations. In the other side, and, particularly, when a long time propagation is need, it must be exigible the use of numerical methods that supply the solution showing a qualitative behaviour as close as possible to the exact solution; this behaviour can be realized by means of backward error analysis. It is checked that the partitioned symplectic integrators, particularly, the Lobatto IIIA-IIIB, are well adapted to the propagation of differential problems with constrains, because they preserve some integrals of motion as well as the constrains. The use of the propagators and the formulation just mentioned allows us to advance one more step in the long time propagation orbits.