7 - Lagrange’s Equations

Summary

The simplest version of the Lagrange's equations (valid only for holonomic systems whose motion is described through the time derivative of coordinates) is presented as an analytically systematized version of the method of virtual power. They provide the equations of motion of the system from the derivatives of its mechanical energy and the generalized forces associated with the nonconservative interactions. Two methods to calculate the constraint unknowns are given. The first one is based on that simple version of the Lagrange's equations, while the second one leads to the Lagrange's equations with multipliers. Hamilton's principle is presented as the gateway to analytical dynamics. Finally, the equilibrium configurations of an n degree of freedom system are considered.