Lagrangian-mechanics

The Lagrangian Method, Morin

The Euler-Lagrange Equation: $\boxed{\frac{\partial \mathcal{L}}{\partial q}-\frac{d}{dt}\left(\frac{\partial \mathcal{L}}{\partial \dot{q}}\right)=0}$ where the the Lagrangian can be defined for a monogenic system as: $\boxed{\mathcal{L}=T(q_i,\dot{q_i},t)-V(q_i,\dot{q_i},t)}$ with initial conditions $q_i(t_1)$ and $q_i(t_2)$