Chapter 2: Lagrangian Mechanics

The elementary formulation of mechanics given in the previous chapter presumes that the forces are known. In practice, however, one very often encounters situations where some of the forces are not known a priori. This typically involves constraints that limit the allowed motion such that, in many instances, one may not be able to formulate the corresponding constraining forces independent of the dynamical situation. In such cases, one needs to adapt Newton’s second law so that the determination of the constraining forces becomes an integral part of the solution of the equations of motion. The formal framework to achieve this is furnished by the Lagrangian approach to mechanics, named after Joseph Louis Lagrange.