Angular velocity

The angular velocity of a point particle or rigid body describes the rate at which its orientation changes. It is analogous to translational velocity, and is defined in terms of the derivative of orientation with respect to time, just as translational velocity is the derivative of displacement with respect to time. It is customary to introduce the concept of velocity by first defining average velocity as displacement divided by time. There the analogy with angular velocity is less useful: for example, if a body is rotating at a constant angular velocity of one revolution per minute, then over a one-minute period the 'average angular velocity' of the body is zero, because the orientation is exactly the same at the beginning of the time period as it is at the end.

Related Topics:
Rigid body - Orientation - Translational velocity - Derivative

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More precisely, if A(t) is the special orthogonal linear transformation which describes the orientation, the angular velocity is defined as A(t)^{-1}{dover dt}A(t). It follows that angular velocity is a skew-adjoint linear transformation . It is useful to restrict attention to two or three dimensions and represent the three-dimensional Lie algebra of skew-adjoint linear transformations of V{}_3(R) by R³. The commutator operation, which is the Lie product of the algebra, is represented by the cross product in R³. The rest of this article is devoted to a discussion in that style.

Related Topics:
Special orthogonal linear transformation - Skew-adjoint linear transformation - Represent - Lie algebra - Commutator - Cross product

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