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On consequences of the principle of stationary action for dissipative bodies

Kosiński W., Perzyna P.

Archives of Mechanics

2012

Vol. 64, nr 1

95-106

The aim of this note is to show possible consequences of the principle of stationary action formulated for dissipative bodies. The material structure with internal state variables is considered for those bodies. The appropriate action functional is proposed for a typical dissipative body. Possible variations of fields of dependent state variables are introduced together with a non-commutative rule between operations of taking variations of the field and their partial time derivatives. Assuming vanishing of the first variation of the functional, the balance of linear momentum in differential form is received together with evolution equations for internal state variables and stress boundary condition.

Stationary Action Principle for Vehicle System with Damping

Kosiński W., Oliferuk W.

Acta Mechanica et Automatica

2012

Vol. 6, no. 4

23-26

The aim of this note is to show possible consequences of the principle of stationary action formulated for nonconservative sys tems. As an example, linear models of vibratory system with damping and with one and two degrees of freedom are considered. This kind of models are frequently used to describe road and rail vehicles. There are vibrations induced by road profile. The appropriate action functional is proposed with the Lagrangian density containing: the kinetic and potential energies as well as dissipative one. Possible variations of generalized coordinates are introduced together with a noncommutative rule between operations of taking variations of the coordinates and their time derivatives. The stationarity of the action functional leads to the EulerLagrange equations.

On a certain extension of the principle of stationary action and its applications

Łaciński Ł., Rychlewska J., Szymczyk J., Woźniak C.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2007

Vol. 6, nr 1

141-145

The aim of this contribution is to propose a certain extension of the principle of stationary action which can be applied to derive the hyperbolic and elliptic PDEs with quasi-linear operators. The proposed generalized form of the above principle will be used to formations of mathematical models for solids and structures.