Lagrange's equations are a set of mathematical formulas used in classical mechanics to describe the motion of a system. They are derived from the principle of least action, which states that the path taken by a system is the one that minimizes the action, a quantity that combines kinetic and potential energy. These equations help simplify complex mechanical problems by focusing on energy rather than forces. The equations are typically expressed in terms of generalized coordinates, which represent the system's configuration. This approach allows for easier analysis of systems with constraints, making it a powerful tool in both theoretical and applied physics.