# Calculating angular acceleration when moment of inertia tensor is singular

I am attempting to simulate the motion of a rigid body composed of point masses in a 3D coordinate system. In doing so, I need to calculate the angular acceleration of the rigid body due to external torque as such

$\boldsymbol{\alpha} = \mathbf{I}^\mathrm{-1} \boldsymbol{\tau}$

where $\boldsymbol{\alpha}$ is the angular acceleration, $\boldsymbol{I}$ is the moment of inertia tensor, and $\boldsymbol{\tau}$ is torque in the body frame. However, when I compose a rigid body of two point masses, the moment of inertia tensor is rank-deficient and thus non-invertible. In this case, how would the angular acceleration be calculated? Would a pseudoinverse suffice?

Anyway, you should find that the component of $\alpha$ along a singular axis has no effect on the motion. Therefore, I expect that a pseudoinverse would work fine. (But I'm not sure.)