This talk considers three interrelated problems. Theseproblems are connected by an underlying mathematical theme,namely the discretization of variational principles in thesense of Moser and Veselov for mechanical systems withsymmetry. The first problem concerns symplectic andmultisymplectic-momentum integration of mechanical systemswith constraints (symplectic DAE solvers), with applicationsto soliton interactions in integrable pde's. The secondproblem deals with collision algorithms in problemsconcerning, for example, playing pool or in fragmentationprocesses, in which complex collision sequences occur. Thethird deals with mission design problems for JPL for whichdynamical systems ideas and optimal control also play animportant role.