Some Surprising Conservative and Nonconservative Moments in the Dynamics of Rods and Rigid Bodies

摘要

Representations for conservative and nonconservative moments in classical mechanics are discussed in this expository article. When the rotation is parameterized by a set of Euler angles, a particularly transparent representation can be found which has ties to classic works in mechanics dating to Lagrange in 1780 and joint coordinate systems that are commonly used in orthopaedic biomechanics. The article also surveys connections between Lagrange's equations of motion and the Newton-Euler equations of motion. A variant on the Lagrange top and a satellite dynamics problem are presented to illustrate some of the key concepts discussed in the paper.