HW12 prob4 two cones

HW12 prob4 two cones - Problem Inertia Tensor and Kinetic...

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Problem Inertia Tensor and Kinetic Energy of Two Cones Joined at Their Tips The two cones are joined at their tips. Each cone is a prolate ellipsoid with I 1 = I 2 >I 3 . One cone is oriented with its principal symmetry axis along the x axis of a body frame, while the other cone has its symmetry axis along the y axis of the body frame. Because the inertia tensor is extensive in the mass, the inertia tensor for this composite body is simply the sum of the inertia tensors for the two separate bodies. For the cone along the x axis, we have I ( x ) = I 3 00 0 I 1 0 00 I 1 , (1) and for the cone along the y axis, we write I ( y ) = I 1 00 0 I 3 0 00 I 1 . (2) In both Eqs.(1) and (2) we see that the location of I 3 depends upon the orien- tation of the cone along the body axes. Adding Eqs.(1) and (2), we obtain the inertia tensor for the composite system I = I 1 + I 3 00 0 I 1 + I 3 0 00 2 I 1 . (3) This tells us that the original coordinateaxesst i l lserveaspr inc ipa laxes

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HW12 prob4 two cones - Problem Inertia Tensor and Kinetic...

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