A discrete multisymplectic fabric model
Bensoam, Joël Khan, Shiraz Chirikjian, Gregory S
Bensoam, Joël
Khan, Shiraz
Chirikjian, Gregory S
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Robotics
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Journal article
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English
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Abstract
A variety of engineering problems require a robust numerical framework for modeling fabrics. In this article, Cartan’s method of moving frames is used to design variational integration techniques for fabrics, modeling the fabric as an inextensible surface, free of any normal stress, that is subject to the influence of gravity. In addition, we use Noether’s theorem to derive the invariant quantities (i.e., Noether currents) associated with the symmetries of the fabric. It is shown that these invariants correspond to the extension of the well-known Young-Laplace law in presence of gravity. The theory is applied to design two types of integrators: (i) a semi-analytic integrator is proposed for axisymmetric boundary value problems, and (ii) a general covariant multisymplectic integrator is derived. Unlike the existing works on multisymplectic integrators, the proposed integrators address the non-separability of the Lagrangian energy functional with respect to the two independent variables. Finally, numerical simulations are used to validate our findings.
Citation
J. Bensoam, S. Khan, G.S. Chirikjian, "A discrete multisymplectic fabric model," Communications in Nonlinear Science and Numerical Simulation, vol. 159, pp. 109852-109852, 2026, https://doi.org/10.1016/j.cnsns.2026.109852.
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Communications in Nonlinear Science and Numerical Simulation
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49 Mathematical Sciences, 4901 Applied Mathematics
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Elsevier