 They can be in the form of arc lengths or angles.They are a considerable simplification to describe motion, since they take advantage of the intrinsic constraints that limit the system's motion, and the number of coordinates is reduced to a minimum.The time derivatives of the generalized coordinates are the "generalized velocities"

The Euler–Lagrange equations are

where the "Lagrangian" is a function of the configuration and its time rate of change (and possibly time )

Setting up the Lagrangian of the system, then substituting into the equations and evaluating the partial derivatives and simplifying, a set of coupled second order ODEs in the coordinates are obtained.