Inverse variational problem for non-standard Lagrangians

Abstract

The non-standard Lagrangians (NSLs) for dissipative-like dynamical systems were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity and (iii) Lokta-Volterra model. We point out that our method is quite general for applications to other physical systems.

6 pages, no figures

References in corpus (2)

• A direct approach to the construction of standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients
• Lagrangians Galore

Cited by in corpus (10)

• Special Functions of Mathematical Physics: A Unified Lagrangian Formalism
• Lagrangian formalism and Lie group approach for commutative semigroup of differential equations
• Nonstandard Null Lagrangians and Gauge Functions and Dissipative Forces in Dynamics
• Nonstandard Null Lagrangians and gauge Functions for Newtonian Law of Inertia
• General Null Lagrangians and Their Novel Role in Classical Dynamics
• New Role of Null Lagrangians in Derivation of Equations of Motion for Dynamical Systems
• The role of the massless phantom term in the stability of a non-topological soliton solution
• On the analytic representation of Newtonian systems
• Quantization of nonlinear non-Hamiltonian systems
• Faster-Than-Light Solitons in 1 + 1 Dimensions