In these lectures the planar problem of three bodies with masses $m_0$, $m_1$, $m_2$ will be used as a model of coorbital motion, thus leaving the analysis of three-dimensional effects to later work. For theoretical as well as for numerical studies the choice of appropriate variables is essential. Here Jacobian coordinates and a rotating frame of reference will be used. The application of the Hamiltonian formalism in connection with complex ...

The continuously growing computing power of modern computers admits to tackle numerical problems of extreme complexity. This complexity carries over to the numerical methods applied to solve the problems. Whereas the mathematical formulation of these methods does not raise any difficulties, their implementation turns out to be the bottleneck in the realization of numerical applications. In the last years, in order to afford relief, object ...