Speaker
Description
Various approaches exist to preserve the underlying geometric structures of mechanical systems under spatial discretization or numerical integration. They can be constructed to guarantee symplecticity of the discrete Hamiltonian flow, to respect the manifold structure of the configuration space (both is true in Lie group variational integrators, see e.g. [1]), or to preserve the energy balance. In a multi-body system, different parameterizations of the configuration space are possible: minimal coordinates, which intrinsically satisfy the kinematic constraints, redundant coordinates, which require the explicit handling of the algebraic constraint equations, or the solution update on the configuration manifold, as in global schemes on Lie groups. A simple planar pendulum is used in [2] to illustrate the application of their energy and constraint-preserving Petrov-Galerkin numerical integration approach to constrained mechanical systems, written in a form generalizing Hamiltonian and gradient systems. In this talk, we present the application of the scheme to planar serial multi-body systems with multi-articular elastic couplings, whose potential energy contribution can nicely be expressed through the chosen Cartesian coordinates. We provide comparisons with the integration of minimal models in joint coordinates and global formulations on the configuration manifold.
[1] Herrmann, M. and Kotyczka, P. "Relative-kinematic formulation of geometrically exact beam dynamics based on Lie group variational integrators". Computer Methods in Applied Mechanics and Engineering, vol. 432 A, 2024, article 117367.
doi: 10.1016/j.cma.2024.117367.
[2] Egger, H., Habrich, O. and Shashkov, V. "On the Energy Stable Approximation of Hamiltonian and Gradient Systems" Computational Methods in Applied Mathematics, vol. 21, no. 2, 2021, pp. 335-349. doi: 10.1515/cmam-2020-0025.
