Derivative of Rotation Matrix Direct Matrix Derivation of Well Known Formula

Fumio Hamano

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arXiv · 1311.6010

Derivative of Rotation Matrix Direct Matrix Derivation of Well Known Formula

Fumio Hamano

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Abstract

In motion Kinematics, it is well-known that the time derivative of a 3x3rotation matrix equals a skew-symmetric matrix multiplied by the rotation matrix where the skew symmetric matrix is a linear (matrix valued) function of the angular velocity and the rotation matrix represents the rotating motion of a frame with respect to a reference frame. The equation is widely used in engineering, e.g., robotics, control, air/spacecraft modeling, etc. However, the derivations found in the literature are indirect. Motivated by the fact that the set of 3x3rotation matrices, i.e., SO(3), is a Lie group, forming a smooth (differentiable) manifold, we describe the infinitesimal increment of the rotation matrix in terms of rotation matrices and show that the above equation immediately follows.

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Fumio Hamano. 2013-11-23. Derivative of Rotation Matrix Direct Matrix Derivation of Well Known Formula. https://arxiv.org/abs/1311.6010

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