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for unit quaternions used to represent rotations for 3D prove that : a) quaternion conjugate corresponds to...

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Advance Math

for unit quaternions used to represent rotations for 3D provethat :

a) quaternion conjugate corresponds to rotation inverse (Approach 1: negate the angle in the formula for converting from theaxis-angle form and apply trigonometric identities. Approach 2:convincingly discusses what negating and axis description does interms of rotation effects and in terms of the formula)

b) negated quaternions represent the same rotation ( hint: add2PI to the rotation angle in the axis angle formula, explain whatthat means in terms of orientation, and apply trigonometricidentities

Answer & Explanation Solved by verified expert
3.8 Ratings (433 Votes)
We first solve this using a grouptheoretic approachThe group is isomorphicto the quaternions of unit norm via the following mapNow identify withthe span of Now if and then And we    See Answer
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