CAPA-seminarium: Long term dynamics and crossing singularities in the restricted N-body problem

  • Datum:
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Stefano Marò
  • Kontaktperson: Alejandro Luque
  • Seminarium

Abstract: We consider the long term dynamics of the restricted N body problem, modeling the dynamics of an asteroid moving in the gravitational field of the Solar system. The asteroid evolution is computed by averaging over the fast angles using standard techniques of perturbation theory. We focus on the critical case where the trajectory of the asteroid crosses the one of a planet during the evolution. This produces a singularity in the averaged equations of motion. We prove that the averaged vector field can be extended to two Lipschitz continuous vector fields in a neighborhood of crossing configurations and we define generalized solutions, going beyond this singularity. Moreover, we prove that the orbit distance between the asteroid and a planet is differentiable also in case of crossings.  We will consider the non-resonant regime and extend the theory to the resonant regime. We will give some applications and conclude with a comparison with other models present in literature. Joint work with Giovanni Gronchi.