Lie Group Variational Integrator for the Geometrically Exact Rod with Circular Cross-Section Incorporating Cross-Sectional Deformation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917268150026240 |
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| author | Siddharth, Srishti Natarajan, Vivek Banavar, Ravi N. |
| author_facet | Siddharth, Srishti Natarajan, Vivek Banavar, Ravi N. |
| contents | In this paper, we derive the continuous space-time equations of motion of a three-dimensional geometrically exact rod, or the Cosserat rod, incorporating planar cross-sectional deformation. We then adopt the Lie group variational integrator technique to obtain a discrete model of the rod incorporating both rotational motion and cross-sectional deformation as well. The resulting discrete model possesses several desirable features: it ensures volume conservation of the discrete elements by considering cross-sectional deformation through a local dilatation factor, it demonstrates the beneficial properties associated with the variational integrator technique, such as the preservation of the rotational configuration, and energy conservation with a bounded error. An exhaustive set of numerical results under various initial conditions of the rod demonstrates the efficacy of the model in replicating the physics of the system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_10963 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lie Group Variational Integrator for the Geometrically Exact Rod with Circular Cross-Section Incorporating Cross-Sectional Deformation Siddharth, Srishti Natarajan, Vivek Banavar, Ravi N. Systems and Control Numerical Analysis Robotics In this paper, we derive the continuous space-time equations of motion of a three-dimensional geometrically exact rod, or the Cosserat rod, incorporating planar cross-sectional deformation. We then adopt the Lie group variational integrator technique to obtain a discrete model of the rod incorporating both rotational motion and cross-sectional deformation as well. The resulting discrete model possesses several desirable features: it ensures volume conservation of the discrete elements by considering cross-sectional deformation through a local dilatation factor, it demonstrates the beneficial properties associated with the variational integrator technique, such as the preservation of the rotational configuration, and energy conservation with a bounded error. An exhaustive set of numerical results under various initial conditions of the rod demonstrates the efficacy of the model in replicating the physics of the system. |
| title | Lie Group Variational Integrator for the Geometrically Exact Rod with Circular Cross-Section Incorporating Cross-Sectional Deformation |
| topic | Systems and Control Numerical Analysis Robotics |
| url | https://arxiv.org/abs/2602.10963 |