“…With some abuse of notation we denote the force and the cost functions defined on T * Q × U and T * Q, respectively, by F (q, p, u) := F (q, f (q, p), u), C(q, p, u) := C(q, f (q, p), u) and Φ(q, p) := Φ(q, f (q, p)) such that Problem 2.1 can be formulated as an optimal control problem for the partitioned system (6). subject toq…”