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Three-Dimensional Rotation Matrices

Physics 216 Spring 2012. Three-Dimensional Rotation Matrices 1. Rotation Matrices A real orthogonal matrix R is a matrix whose elements are real numbers and satisfies 1. R = RT (or equivalently, RRT = I, where I is the n n identity matrix). Taking the determinant of the equation RRT = I and using the fact that det(RT ) = det R, it follows that (det R)2 = 1, which implies that either det R = 1 or det R = 1. A. real orthogonal n n matrix with det R = 1 is called a special orthogonal matrix and provides a matrix representation of a n-dimensional proper rotation1 ( no mirrors required!)

Three-Dimensional Rotation Matrices 1. Rotationmatrices ... where your fingers point in the θ direction. Then, your thumb ... since the rotation angle is the only non-trivial scalar quantity in this problem. If we also allow for transformations between right-handed and left-handed orthonormal

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