Transfer Matrix Method for Multibody Systems

Appendix IRotation Formula Around an Axis

Consider that A is a right‐handed inertia coordinate system with unit orthogonal bases i, j and k, and B is a right‐handed body‐fixed coordinate system with unit orthogonal bases i₁, j₁ and k₁. is any vector fixed in A and is a vector fixed in B and equal to prior to the motion of B in A. is a unit vector whose orientation relative to both A and B remains unaltered throughout the motion, and the radian measure θ is the angle when B rotates relative to A. Let and , as shown in Figure AI.1.

Figure AI.1 A inertia system rotating angle θ around .

The plane π ₁ contains point E and is perpendicular to vector , and point O ₁ is the intersection ...