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arXiv · 2504.00866

Virtual nonlinear nonholonomic constraints from a symplectic point of view

Efstratios Stratoglou·Alexandre Anahory Simoes·Anthony Bloch·Leonardo Colombo
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Abstract

In this paper, we provide a geometric characterization of virtual nonlinear nonholonomic constraints from a symplectic perspective. Under a transversality assumption, there is a unique control law making the trajectories of the associated closed-loop system satisfy the virtual nonlinear nonholonomic constraints. We characterize them in terms of the symplectic structure on $TQ$ induced by a Lagrangian function and the almost-tangent structure. In particular, we show that the closed-loop vector field satisfies a geometric equation of Chetaev type. Moreover, the closed-loop dynamics is obtained as the projection of the uncontrolled dynamics to the tangent bundle of the constraint submanifold defined by the virtual constraints.

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Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch, Leonardo Colombo. 2025-04-01. Virtual nonlinear nonholonomic constraints from a symplectic point of view. https://arxiv.org/abs/2504.00866

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