On the relation between the Gyarmati, Prigogine and Hamilton principles

Abstract

The paper shows that both the Hamilton and the Prigogine principle belong to a respective special form of Gyarmati's principle. The Prigogine and Hamilton principles are the limit cases of the Gyarmati principle, so that one can justify that the Gyarmatic principle should be valid not only for the irreversible process, but also for the nondissipative or mixed process. From the simplifled Gyarmati principle the classical expressions of the Hamilton principle can be generalized into a complete set of inequalities. The principle of minimum mechanical energy, the principle of minimum potential energy and the principle of minimum kinetic energy all belong to alternative forms of the Hamilton principle. The dissipative process should be a decelerated process, whereas the non-dissipative process should be an accelerated one. A possibility is suggested to solve the problem of the longitudinal profile of irreversible process by using an alternative expression of the Gyarmati principle.