Nonlinear nonholonomic constraints stop bending to noisy data: Chetaev geometry enters the Gaussian-process prior, so predictions meet the acceleration constraint exactly
Data-driven models of mechanical systems under nonlinear nonholonomic constraints often predict accelerations that violate those constraints. This work combines the Lagrange–d’Alembert–Chetaev equations with tangency to the constraint submanifold into an affine space of admissible accelerations, then embeds it in a Gaussian-process prior through a kinetic-energy-metric projector and the Moore–Penrose pseudoinverse, so prior and posterior predictions satisfy the constraints exactly. On a three-dimensional directional flocking benchmark, the model's prediction stays unchanged under constraint-incompatible observation perturbations, while standard and post-projected Gaussian processes degrade as contamination grows.