Lagrangian Dynamics Generalized Coordinates and Forces

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Lagrangian mechanics is a re-formulation of classical mechanics that combines conservation of momentum with conservation of energy. It was introduced by the French mathematician Joseph-Louis Lagrange in 1788.In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, either theLagrange equations of the first kind,which treat constraints explicitly as extra equations, often using Lagrange multipliers;or theLagrange equations of the second kind, which incorporate the constraints directly by judicious choice of generalized coordinates. The fundamental lemma of the calculus of variations shows that solving the Lagrange equations is equivalent to finding the path for which the action functional is stationary, a quantity that is the integral of the Lagrangian over time.

Admissible Variations Virtual Displacements Generalized Coordinates Virtual Work Tethered Cart Holonomic Systems Cart with Pendulum Springs Dashpots