2018•Applied Physics ResearchOpen access

Action Function Formulation for Conservative Systems with Second-Order Lagrangian

Ola A. Jarab’ah

Abstract

The Euler Lagrange equation is studied to obtain the equations of motion for conservative systems with second order Lagrangian. The solutions of these equations are substituted in the given Lagrangian. The action function is then derived by calculating the time integral of the Lagrangian. To explain the application of our formalism two examples are discussed.

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Key concepts: Lagrangian, Inverse problem for Lagrangian mechanics, Action (physics), Formalism (music), Equations of motion, Euler–Lagrange equation, Lagrangian system, Lagrange multiplier