The previous chapter introduced the basic notions of spatial quantities and dealt with the kinematic aspects of spatial algebra. This chapter deals with the dynamic aspects — principally inertia. The spatial momentum of a rigid body is defined, then spatial rigid-body inertia is defined as a mapping between velocity and momentum, and its representation as a 6 × 6 matrix is deduced. The basic operations of transformation, differentiation and combination (i.e., addition) of spatial rigid-body inertias are described, and the equations of motion for a rigid body are given. The concepts of inverse inertias and articulated-body inertias are introduced, and their properties and uses are described. The discussion on inertias is concluded with a brief review of alternative representations of inertia. The ease with which inertias can be manipulated is one of the key features of spatial notation.
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