 Over the 19th century, the application of the least action principle dominated the approach of analytical dynamics to physical problems. Lagrangian mechanics seeks to determine the trajectory of a system of particles over time by solving Lagrangian equations for the system. These equations are formulated using the least action principle. In the Lagrangian formalism, a system of particles follows a path that minimizes the action over time. Lagrange’s equations can be applied easily to systems of polar coordinates and of Cartesian coordinates alike, a reason that the Lagrangian formalism was adopted preferentially over the 19th century. 