A Method for Computing Families of Periodic Orbits Based on Unconstrained Optimization

A new efficient method is presented for the numerical computation of families of periodic orbits of systems with three or more degrees of freedom. This method is based on a well-known procedure using the variational equations as well as on unconstrained optimization techniques. This combination accelerates the convergence of previous schemes. The new composite method has been implemented here on an example of interest to Celestial Mechanics.