Inverse problem for Lagrangian mechanics

The inverse problem for Lagrangian mechanics typically refers to the task of determining the Lagrangian function \( L \) that corresponds to a given set of equations of motion (often expressed as a system of second-order differential equations). This contrasts with the direct problem in Lagrangian mechanics, where the Lagrangian is known and the equations of motion are derived from it using the Euler-Lagrange equations.