Spatial Motion of a Rigid Body

Spatial motion of a rigid body covers motions that cannot be reduced to planar kinematics. The orientation of the body changes in three-dimensional space, so angular velocity and angular acceleration are treated as vectors.

Spherical motion

In spherical motion, one point of the rigid body remains fixed while all other points move on spherical surfaces centered at that point. Instantaneously, the motion may be characterized as rotation about an instantaneous axis.

General rigid-body motion

The general motion of a free rigid body can be decomposed into translation of a selected reference point and rotation of the body relative to that point. This is the three-dimensional counterpart of the decomposition used in plane motion.

Kinematic quantities

Velocities and accelerations of body points are determined from the translational component together with the body's angular velocity and angular acceleration. Vector notation provides a unified description independent of body orientation.