Definition:Rotation (Geometry)/Space/Vector Form
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Definition
A space rotation $r_\theta$ can be expressed as an axial vector $\mathbf r_\theta$ such that:
- the direction of $\mathbf r_\theta$ is defined to be its axis of rotation
- the length of $\mathbf r_\theta$ specifies its angle of rotation of $\mathbf r_\theta$ to an appropriate scale.
Right-Hand Rule
Let $\mathbf V$ be an axial vector acting with respect to an axis of rotation $R$.
Consider a right hand with its fingers curled round $R$ so that the fingers are pointed in the direction of rotation of $\mathbf V$ around $R$.
The right-hand rule is the convention that the direction of $\mathbf V$ is the direction in which the thumb is pointing:
Sources
- 1957: D.E. Rutherford: Vector Methods (9th ed.) ... (previous) ... (next): Chapter $\text I$: Vector Algebra: $\S 3$