In classical mechanics, the Principle of Least Action states that the path taken by a system is the one where the action is minimized, indicating that forces acting on the system do not influence its trajectory.

The Principle of Least Action does not say that forces are ignored; instead, the forces appear inside the Lagrangian through the potential energy term, so the action depends on them. By varying the action, we obtain the Euler–Lagrange equations, which are exactly Newton’s equations that include the forces acting on the system. Thus the path that makes the action stationary is the one that satisfies the correct equations of motion, not one where forces are absent. For example, for a mass on a spring, the Lagrangian \(L=\tfrac12mv^2-\tfrac12 kx^2\) leads to the equation \(m\ddot x=-kx\), showing the spring force determines the trajectory. In short, the principle incorporates forces and predicts the trajectory that satisfies Newton’s laws.