The action principle for dissipative systems

Abstract

In the present work we redefine and generalize the action principle for dissipative systems proposed by Riewe by fixing the mathematical inconsistencies present in the original approach. In order to formulate a quadratic Lagrangian for non-conservative systems, the Lagrangian functions proposed depend on mixed integer order and fractional order derivatives. As examples, we formulate a quadratic Lagrangian for a particle under a frictional force proportional to the velocity, and to the classical problem of an accelerated point charge.

References in corpus (5)

• Can the dark energy equation-of-state parameter w be less than -1?
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Effective Lagrangians with Higher Order Derivatives
• Fractional variational problems depending on indefinite integrals
• Testing symmetries in effective models of higher derivative field theories

Cited by in corpus (9)

• An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems
• Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems
• Generalized nonconservative gravitational field equations from Herglotz action principle
• Dark energy with zero pressure: Accelerated expansion and large scale structure in action-dependent Lagrangian theories
• Noether-type theorem for fractional variational problems depending on fractional derivatives of functions
• Dissipation in Langevin Equation and Construction of Mobility Tensor from Dissipative Heat Flow
• Quantization of nonlinear non-Hamiltonian systems
• The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only
• When action is not least for systems with action-dependent Lagrangians