The Lagrangian is a function that summarizes the dynamics of a system in classical mechanics, defined as the difference between kinetic and potential energy. It serves as the foundation for deriving equations of motion through the Euler-Lagrange equations, which arise from the principle of least action. In optimal control theory, the Lagrangian is crucial in formulating problems where one seeks to optimize a certain performance index, often leading to insights about control strategies and system behavior.
congrats on reading the definition of Lagrangian. now let's actually learn it.