Overview
Hamiltonian mechanics is a set of equations that are equivalent to the Newtonian formulation.
Hamiltons Equations
The generalized momentum is defined to be
{% p_i = \frac{\partial{L}}{\partial{\dot{q_i}}} %}
Then the equations of motion can be stated as
{% \frac{dp_i}{dt} = \frac{\partial{L}}{\partial{q_i}} %}