Hamilton's Principle, also known as the principle of stationary action, states that the path taken by a system between two states is the one for which the action is minimized or made stationary. The action is defined as the integral of the Lagrangian, which is the difference between kinetic and potential energy, over time. This principle is fundamental in classical mechanics and provides a powerful method for deriving the equations of motion for a system. In mathematical terms, Hamilton's Principle can be expressed as finding the path that makes the integral of the Lagrangian stationary. This approach leads to Lagrange's equations and is a cornerstone of analytical mechanics. It highlights the deep connection between energy, motion, and the laws governing physical systems.