# Quaternion rotation derivatives?

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for quaternion rotation of a point: newPoint = quaternionOrientation * point * (~quaternionOrientation) where ~ means conjugate what is the derivative of of newPoint with respect to the quaternionOrientation, what is the jacobian? A brief search only turned up time derivative of quaternions. thanks for any help.

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I'd convert the quartinion into a rotation matrix M then we have New = M*Old
dNew/dt = dM/dt*old + M*dOld/dt there are analigious formula for quartiniton diferentions I can't remember them tho. you can't really differentiate something wiht respect to something else that is constant there has to be something indicating how the the quantities are varying with respect to another to differentiate a matrix we simply take the vector derivative of it's basis vectors. what exactly are you applying this to? rigid body stuff?

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The variables I want differentiate with respect to is the parameters of the quaternion.

I am applying it to inverse kinematic, where the rotated point is the end effector and the quaternion represent the orientation of the joint. Therefore I want to know how change in each of the parameters in the quaternion affects the position of the end effector. I am not looking for derivative with respect to time.

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nevermind I worked it out with the help of matlab symbolic tool box

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