Resumen de La 'descarga artillera' en coordenadas intrínsecas

Martín Lara Coira

• The numerical solution of two-point boundary value problems is usually achieved either by methods where the unknons are the values of the true solution at a grid of points (collocation and finite difference methods), or by shooting methods, that confront the problem as an initial value problem. The usefulness of the first class of methods is evident from the popular package AUTO. With respect to the second class, there is a wealth of methods based on differential corrections. However, when dealing with highly unstable motions, the numerical solution of the differential equations quickly degenerates, preventing the required precision in the shooting solution of the initial value problem. This does not happen to collocation or finite difference methods, for they treat the solution as a whole. The objection to shooting is easily overcome by introducting slight modifications in the algorithms, resulting in 'multiple shooting' methods. In the present work we formulate a multiple shooting algorithm in intrinsic coordinates -a kind of shooting that exhibits some advantages for the analytical continuation of periodic orbits in conservative dynamical systems of three degrees of freedom.