Hamilton's Equations of Motion

$$\{\begin{array}{c}\frac{\partial }{\partial q_i}H=-{\dot{p}}_i\\ \frac{\partial }{\partial p_i}H={\dot{q}}_i\end{array}$$

Where:

• $H$ is the classical hamiltonian
• $q_i$ is the position of the $i$th Particle.
• $p_i$ is the momentum of the $i$th Particle.