Class 42: Free symmetric top Class 42: Free symmetric top
Free symmetric top in body frame Assume = = (symmetric) and no external torque acting on the top: Assume 1 = 2 = (symmetric) and no external torque acting on the top: In the body frame: precesses about e 3 e 3 B (stationary) with angular velocity B and sweeps out y p B the body cone Body cone ( ( 3 ) ) e 2 2 3 3 3 B e 1
Free symmetric top in space frame Assume = = (symmetric) and no external torque acting on the top: Assume 1 = 2 = (symmetric) and no external torque acting on the top: z z L S L S e 3 Body cone e 3 B Space cone Space cone B Body cone y Body cone Body cone Body cone Body cone y y For > 3 (Tall thin top) ( For < 3 (Short fat top) ( h ll hi ) f ) x x In the space frame: p L , , and e 3 are in the same plane. L is L S stationary (conservation of angular momentum), is precessing about L and sweeps out the space cone with an anglar t th ith l velocity S . The body cone is rolling on the space cone with at the line of contact.
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