Title :
A variational formulation for dissipative systems
Author :
Homsup, N. ; Homsup, W.
Author_Institution :
Dept. of Electr. Eng., Kasetsart Univ., Bangkok, Thailand
Abstract :
It is well known that classical Lagrangians do not exist for dissipative systems. The paper presents three formulations of a mathematical Lagrangian for a dissipative system. The first one depends on the generalized coordinate x, its velocity x˙, the image variable y and its velocity y˙. This Lagrangian can be obtained directly from differential equations of a dynamic system. For linear reciprocal dissipative systems, the image variable can be substituted by the generalize coordinate with reversed time scales. The second formulation which can resolve the problem for nonlinear dynamical systems depends on kinetic energy, potential energy, and the time integral of a dissipation function. The last formulation which is a time dependent function can be obtained for a special type of linear system
Keywords :
differential equations; nonlinear dynamical systems; variational techniques; differential equations; dissipation function; generalize coordinate; generalized coordinate; image variable; kinetic energy; linear reciprocal dissipative systems; linear system; mathematical Lagrangian; nonlinear dynamical systems; potential energy; reversed time scales; time dependent function; time integral; variational formulation; velocity; Differential equations; Energy resolution; Integral equations; Kinetic energy; Kinetic theory; Lagrangian functions; Linear systems; Nonlinear dynamical systems; Nonlinear equations; Potential energy;
Conference_Titel :
System Theory, 1997., Proceedings of the Twenty-Ninth Southeastern Symposium on
Conference_Location :
Cookeville, TN
Print_ISBN :
0-8186-7873-9
DOI :
10.1109/SSST.1997.581710