## Lagrange Mechanics

For most system, the Lagrange function is $L = T – V$, where T is kinetic energy of the system and V is potential energy of the system. Euler-Lagrange Equation for $L(t,q_1 , … , q_n , \dot{q_1}, … , \dot{q_n})$ is: $$\frac{\partial L}{\partial q_i} = \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q_i}} \right), \, i = 1, … , n$$ In …