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Dynamics_Part72

Dynamics_Part72 - Iy = Iy m x2 z 2 = = = 3 9 m r2 4h2 3 48...

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I y = I I y + m D x 2 + z 2 i = 3 20 m D r 2 + 4 h 2 i + 9 16 mh 2 = 3 20 mr 2 + 48 80 mh 2 + 45 80 mh 2 = 3 20 mr 2 + 93 80 mh 2 = 3 80 m D 4 r 2 + 31 h 2 i I z = I I z + m D x 2 + y 2 i = 3 10 mr 2 + 0 = 3 10 mr 2 Thus, the moment of inertia tensor relative to the cone’s tip is [ I ] = 3 80 m D 4 r 2 + 31 h 2 i 0 0 0 3 80 m D 4 r 2 + 31 h 2 i 0 0 0 3 10 mr 2 (c) The angular momentum vector is the product of the moment of inertia tensor and the absolute angular- velocity vector, which is the sum of = i and ω = ω k , viz., H O = [ I ] ω = 3 80 m D 4 r 2 + 31 h 2 i 0 0 0 3 80 m D 4 r 2 + 31 h 2 i 0 0 0 3 10 mr 2 l 0 ω M = 3 80 m D 4 r 2 + 31 h 2 i 0 3 10 mr 2 ω Thus, in standard vector form, we have H O = 3 80 m D 4 r 2 + 31 h 2 i i + 3 10 mr 2 ω k (d) The absolute rate of change of H O is given by the Coriolis Theorem, i.e.,
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