Virtual nonlinear nonholonomic constraints from a symplectic point of view
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910900952236032 |
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| author | Stratoglou, Efstratios Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo |
| author_facet | Stratoglou, Efstratios Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00866 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Virtual nonlinear nonholonomic constraints from a symplectic point of view Stratoglou, Efstratios Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo Differential Geometry Optimization and Control 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. |
| title | Virtual nonlinear nonholonomic constraints from a symplectic point of view |
| topic | Differential Geometry Optimization and Control |
| url | https://arxiv.org/abs/2504.00866 |