The Lagrange Equation is a fundamental equation in classical mechanics that describes the motion of a system. It is derived from the principle of least action, which states that the path taken by a system between two states is the one that minimizes the action. The equation is expressed in terms of the Lagrangian, a function that represents the difference between the kinetic and potential energy of the system. In mathematical terms, the Lagrange Equation is formulated as L(q, \dotq, t) , where q represents the generalized coordinates, \dotq represents the generalized velocities, and t is time. By applying this equation, one can derive the equations of motion for complex systems, making it a powerful tool in both theoretical and applied physics.