Kinematics of Rotation

Abstract This chapter deals with techniques needed to define the location and orientation of a moving rigid body. Rigid bodies are characterised and the center of mass of a rigid body is discussed along with rotation operators, rotation matrices, some properties of rotation operators, proper and improper rotation operators, rotation group, kinematics of a rigid body, differentiation of a rotation operator, angular velocity vector, velocities of the masses of a rigid body, Savio’s theorem, infinitesimal rotation, addition of angular velocities, fundamental generators of rotations, rotation with a fixed axis, expansion of fixed-axis rotation, eigenvectors of the fixed-axis rotation operator, Euler theorem, rotation of operators, rotation of the fundamental generators, rotation of a fixed-axis rotation, parameterisation of rotation operators, differentiation of parameterised operator, Euler angles, fixed-axis rotation from Euler angles, time derivative of a product, angular velocity from Euler angles, active and passive rotations, passive transformation of vector components, passive transformation of matrix elements, body derivative, passive rotations and rigid bodies, and passive use of Euler angles.