Hamilton's Principle

States that particles follow the path that minimizes their action. Historically, Hamilton’s principle was postulated after Lagrangian mechanics were derived, but it may be used to define Lagrangian mechanics

$\delta S[q(t)]=0$

• $S$ is the action of the system
• $q(t)$ is the generalized coordinates of the system with respect to time
• States that to find $q(t)$, you need to find the minimum of the action