Direction Cosine Matrix Euler Integration Failure

An example showing why a simple scheme can't be used to integrate angular rates to get orientation. Using Euler's methods to integrate the kinematics doesn't preserve SO(3) symmetry. Using the Lie group generators for rotation in each time step gives you a determinant that goes as 1+theta^2, so the method is doomed from the get-go.

You can correct for this at each time step (by enforcing orthogonality and unit vectors in each column of the matrix) to come up with a workable scheme, but what you really need is an integrator that preserves the SO(3) symmetry of the direction cosine matrix.

You also really need a droid that understands the binary language of moisture vaporators.