Constants of the motion for nonslipping tippe tops and other tops with round pegs

New and more illuminating derivations are given for the three constants of the motion of a nonsliding tippe top and other symmetric tops with a spheri cal peg in contact with a horizontal plane. Some rigorous conclusions about the motion can be drawn immediately from these constants. It is shown that the system is integrable, and provides a valuable pedagogical example of s uch systems. The equation for the tipping rate is reduced to one-dimensiona l form. The question of sliding versus nonsliding is considered. A careful literature study of the work over the past century on this problem has been done. The classic work of Routh has been rescued from obscurity, and some misstatements in the literature are corrected. (C) 2000 American Associatio n of Physics Teachers.