Problem 44830. Twists in 2D

So far we have represented the pose of an object in the plane using a homogeneous transformation, a 3x3 matrix belonging to the special Euclidean group SE(2), which is also a Lie group.

An alternative, and compact, representation of pose is as a twist, a 3-vector comprising the unique elements of the corresponding 3x3 matrix in the Lie algebra se(2). The matrix exponential of the Lie algebra matrix is a Lie group matrix.

Given a homogeneous transformation, return the corresponding twist as a column vector with the translational elements first.