Drake
Spatial Algebra

## Detailed Description

Multibody dynamics involves both rotational and translational quantities, for motion, forces, and mass properties.

It is much more effective to group related rotational and translational quantities together than to treat them independently. We call such groupings spatial quantities.

Here we describe the important spatial quantities used in Drake's multibody mechanics implementation, the terminology and notation we use to document them, and their physical representations in code, typically as Eigen objects.

Next topic: Spatial Pose and Transform

## Modules

Spatial Pose and Transform
A spatial pose, more commonly just pose, provides the location and orientation of a frame B with respect to another frame A.

Spatial Vectors
Spatial vectors are 6-element quantities that are pairs of ordinary 3-vectors.

Spatial Mass Matrix (Spatial Inertia)
A Spatial Mass Matrix (also called Spatial Inertia) M represents the mass, center of mass location, and inertia in a single 6×6 symmetric, mass-weighted positive definite matrix that logically consists of four 3×3 submatrices.