# 2.4 Spatial vectors and inertias

The velocities, forces and inertias associated with 3D coordinate frames and rigid bodies are represented using the 6 DOF spatial quantities described in Sections A.5 and A.6. These are implemented by classes in the package maspack.spatialmotion.

Spatial velocities (or twists) are implemented by Twist, which exposes its translational and angular velocity components through the publicly accessible fields v and w, while spatial forces (or wrenches) are implemented by Wrench, which exposes its translational force and moment components through the publicly accessible fields f and m.

Both Twist and Wrench contain methods for algebraic operations such as addition and scaling. They also contain transform() methods for applying rotational and rigid transforms. The rotation methods simply transform each component by the supplied rotation matrix. The rigid transform methods, on the other hand, assume that the supplied argument represents a transform between two frames fixed within a rigid body, and transform the twist or wrench accordingly, using either (A.27) or (A.29).

The spatial inertia for a rigid body is implemented by SpatialInertia, which contains a number of methods for setting its value given various mass, center of mass, and inertia values, and querying the values of its components. It also contains methods for scaling and adding, transforming between coordinate systems, inversion, and multiplying by spatial vectors.