Equations of motion describing dissipative dynamical systems with coefficients varying either in time or in space are considered. To identify the equations that admit a Lagrangian description, two classes of non-standard Lagrangians are introduced and general conditions required for the existence of these Lagrangians are determined. The conditions are used to obtain some non-standard Lagrangian...

A coupled spring-pendulum system in a conservative field was studied where the equation of motion using Lagrangian and Hamiltonian were obtained. The represented by second-order differential from three generalized coordinate used. potential energy equal to zero when is its equilibrium position. that being used angle first pendulum θ_1, second θ_2, increase length spring x. resulting can be dete...

Taking the Stückelberg Lagrangian associated with the abelian selfdual model of P. K. Townsend et al as a starting point, we embed this mixed firstand second-class system into a pure first-class system by following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin. The resulting Lagrangian possesses an extended gauge invariance and provides a non-trivial example...

The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the...

The Lagrangian star is a germ of the system ({L1, . . . , Lk}, p̃) of Lagrangian submanifolds in the symplectic manifold (M,ω). We investigate the symplectic group action on Lagrangian stars and construct the basic invariants of such action. The Kashiwara signature for 3-Lagrangian linear stars is generalized to the nonlinear case and the generalized contact classes for Lagrangian stars are cons...