The main Hamiltonian function and optimality conditions

The basic principles of analytical mechanics such as the least action and release from links (relaxation) used originally in [1,2] to solve dynamic optimal control problems may lead to sufficient conditions in these problems. They help derive Hamilton — Jakobi (Isaacs — Bellman) equations in optimal control problems. Relations, between Hamilton , Isaacs — Bellman, and Rozonoer functions are established. The Krotov optimality principle may also be interpreted in terms of analytical mechanics.