  In many real-world settings, image observations of freely rotating 3D rigid
bodies, such as satellites, may be available when low-dimensional measurements
are not. However, the high-dimensionality of image data precludes the use of
classical estimation techniques to learn the dynamics and a lack of
interpretability reduces the usefulness of standard deep learning methods. In
this work, we present a physics-informed neural network model to estimate and
predict 3D rotational dynamics from image sequences. We achieve this using a
multi-stage prediction pipeline that maps individual images to a latent
representation homeomorphic to $\mathbf{SO}(3)$, computes angular velocities
from latent pairs, and predicts future latent states using the Hamiltonian
equations of motion with a learned representation of the Hamiltonian. We
demonstrate the efficacy of our approach on a new rotating rigid-body dataset
with sequences of rotating cubes and rectangular prisms with uniform and
non-uniform density.
