In this lesson, you will learn:

  1. About constraints, degrees of freedom, and definition of generalized coordinates

  2. Use of D’ Alembert’s principle to eliminate the forces of constraints

  3. Use of independence of generalized coordinates to arrive at a new form of equations of motion

  4. For systems with forces derivable from a potential, or a generalized potential, the equations of motion take the Euler Lagrange form:
    $$\frac d {dt} \left( \frac {\partial L} {\partial \dot q_k} \right) - \frac {\partial L} {\partial q_k} = 0.$$

  5. For a system of particles with forces derived from a potential energy function V (q) , the Lagrangian is given by L = T − V .