Rigid Body Kinematics

Abstract

Kinematics of positions and of continuous motions of a rigid body: Coordinates used for describing the angular orientation of a body are direction cosines, Euler angles, Bryan angles, axis and angle of a rotation and Euler-Rodrigues parameters. Formulas for the conversion from one set of coordinates to another. Quaternion of a rotation. Quaternion of the resultant of two successive rotations. Angular velocity and angular acceleration. Relationships between motion and inverse motion. Instantaneous screw axis and pitch. Painlev\'e's theorem on the raccording motion of two axodes generated by the instantaneous screw axis. Striction point and distribution parameter of the axodes expressed in terms of position, velocity, acceleration, angular velocity and angular acceleration. Kinematic differential equations relating angular velocity to the rate of change of coordinates of angular orientation (direction cosines, Euler angles, Bryan angles, Euler-Rodrigues parameters).