L'espai de fases del sistema Sol-Terra-Mart-Júpiter

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Gerardo Gómez Muntané ; [en] In this work we study the dynamics of a small particle moving in the Earth-Mars neighbourhood under the gravitational influence of the Sun, the Earth, Mars and Jupiter. To do so, we use a restricted 5-body 2-dimensional model and integrate, using this model, a very large set of initial conditions in order to determine their sensibility with respect to initial conditions. To quantify the sensibility, we use Finite Time Lyapunov Exponents for a time interval of 100 years, and for the numerical propagation we use the ODEX integrator in a parallelized environment, using the CPUs cluster HIDRA of the Departament de Matemàtiques i Informàtica of the Universitat de Barcelona, and OpenMP. The main results are final scalar field for the space phase and the analysis of some of the most interesting structures found.