Summary

• Hamiltonian: $H = \sum p\dot{q} - L$
• Momentum: $p = \frac{\partial L}{\partial \dot{q}}$
• Equations:
  • $\dot{q} = \frac{\partial H}{\partial p}$
  • $\dot{p} = -\frac{\partial H}{\partial q}$
• Describes evolution in phase space
• Foundation for modern physics