Multisymplectic Lie group variational integrator for a geometrically exact beam in \(\mathbb{R}^3\)

DOI10.1016/j.cnsns.2014.02.032zbMath1473.70029arXiv1403.5410OpenAlexW2012085448WikidataQ115358643 ScholiaQ115358643MaRDI QIDQ2300269

Marin Kobilarov, François Demoures, Tudor S. Ratiu, François Gay-Balmaz

Publication date: 27 February 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5410

zbMATH Keywords

energy conservationvariational integratormultisymplectic integratorgeometrically exact beamdiscrete Noether theorem

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Geometric theory, characteristics, transformations in context of PDEs (35A30) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

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Cites Work

• Unnamed Item
• Unnamed Item
• Sensitivity analysis for multibody systems formulated on a Lie group
• A Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternions
• Symmetry reduced dynamics of charged molecular strands
• A finite strain beam formulation. The three-dimensional dynamic problem. I
• A three-dimensional finite-strain rod model. II. Computational aspects
• The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• A Lie-group formulation of kinematics and dynamics of constrained MBS and its application to analytical mechanics
• On one-dimensional finite-strain beam theory: the plane problem
• Discrete mechanics and variational integrators
• Kirchhoff’s problem for nonlinearly elastic rods
• Geometric Numerical Integration
• On the Partial Difference Equations of Mathematical Physics
• Variational methods, multisymplectic geometry and continuum mechanics