arXiv:2607.12627 2026 Dynamics 1 ideas extracted · analyzed Aug 30, 2026
The paper formulates forced mechanics directly on a configuration Lie group, rather than in unconstrained Euclidean coordinates. The transferable asset is the combination of group-valued states, Lie-algebra-valued velocities, and force-driven evolution: neural networks can predict dynamics in a tangent space while the state update remains on the valid manifold through the exponential map. This is particularly useful for rigid-body world models, robotics policies, and generative dynamical models whose states contain rotations or poses, where ordinary additive integration causes drift, invalid rotations, and coordinate singularities.
Replace additive neural state updates for rotations or rigid poses with a learned forced dynamical system whose configuration is updated by Lie-group multiplication. The network predicts body-frame force or acceleration in the Lie algebra, while the exponential map guarantees that every predicted configuration remains on SO(3) or SE(3).