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Class 42: Free symmetric top Class 42: Free symmetric top Free - PowerPoint PPT Presentation

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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:

  1. Class 42: Free symmetric top Class 42: Free symmetric top

  2. 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

  3. 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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