Dynamics of systems with nonintegrable constraints. IV. Integral principles (Q1100946)

[For part III, see the author, ibid. 1983, No.3, 102-111 (1983; Zbl 0516.70017).] Various mathematical models of the motion of mechanical systems with nonintegrable constraints are known. Their validity is demonstrated by limiting processes in systems with no constraints. The general Hamilton- Ostrogradski principle, combined with the technique of limiting process, makes it possible to derive integral principles in the various models of motion of ``unfree'' systems. They are similar formally to Hamilton's principle, but use a different method of variation of motions. The laws of conservation and the conditions of existence of an invariant measure are discussed.