Hamilton's Principle

Hamilton's Principle states that the actual motion of a physical system between two points in time is the one that minimizes (or makes stationary) a quantity called the "action." The action is calculated by integrating the difference between kinetic energy (energy of motion) and potential energy (stored energy) over time. In simple terms, nature chooses the path where this energy difference is balanced in such a way that the total action stays as steady as possible. This principle provides a powerful way to derive the equations governing the motion of mechanical systems.