UC Berkeley

Since their introduction in the early 20th century, the Gibbs– Appell equations have proven to be a remarkably popular and influential method to formulate the equations of motion of constrained rigid bodies. In particular, when the coordinates and quasi-velocities are chosen appropriately, the resulting equations of motion are reactionless even if the constraints on the system are nonholonomic. Researchers provide a demonstration with the help of a recent treatment. The researchers demonstrate that the developments are also applicable to Kane’s equations of motion. They show that it is straightforward to extend the derivation of the Gibbs–Appell equations from the Newton–Euler balance laws.