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szinkopa

angular motion

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If no torque acts on a body then it''s anguar momentum is constant. I have read somewhere that the angular velocity may not be constant in this case. My question is: when isn''t it constant? My guess is: when the inertia tensor is not a diagonal matrix.

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Are you sure you didn''t read that each particle''s linear velocity would be different? Because otherwise if there is no net torque, it would just keep rotating in space until an opposing torque would slow it down...even if the object has a weird shape, if there is no net torque, then the angular velocity should stay constant.

That is just my hunch, I could be totally wrong, in that case I''d learn something new!

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You''re assuming the ''shape'' of the system is constant. If the moment of inertia is changing then the angular velocity will change accordingly. The obvious and most used example of this is to sit on a swivel chair and spin round. Putting your arms out and drawing them in will change the velocity, even with no external torque.

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OK, I see.

And which is better for state variables for angular motion:

orientation and angular velocity OR
orientation and angular momentum

Baraff uses the second. But why?

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I suppose angular momentum is conserved with no external forces, while angular velocity may not be. I would certainly use the second.

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This is from Baraff rigid Body 1:

Angular momentum ends up simplifying equations because it is conserved in nature, while angular velocity is not: if you have a body floating through space with no torque acting on it, the body’s angular momentum is constant. This is not true for a body’s angular velocity though: even if the angular momentum of a body is constant, the body’s angular velocity may not be ! Consequently, a body’s angular velocity can vary even when no force acts on the body. Because of this, it ends up being simpler to choose angular momentum as a state variable over angular velocity.

[edited by - szinkopa on May 28, 2004 10:41:29 AM]

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