BDF integrators for constrained mechanical systems on Lie groups. (English) Zbl 1459.37075
Summary: Multistep methods of BDF type are the method-of-choice in several industrial multibody system simulation packages. In the present paper, BDF is applied to constrained systems in nonlinear configuration spaces with Lie group structure that allows, e.g., a representation of multibody systems with large rotations without singularities. The \(k\)-step Lie group integrator BLieDF avoids order reduction by a slightly perturbed argument of the exponential map for representing the nonlinearity of the numerical flow in the configuration space without any time-consuming re-parametrization.
This integrator is compared with multistep methods on Lie groups suggested by S. Faltinsen et al. [Appl. Numer. Math. 39, No. 3–4, 349–365 (2001; Zbl 0996.65073)] and the advantages of the novel BLieDF integrator are shown.
This integrator is compared with multistep methods on Lie groups suggested by S. Faltinsen et al. [Appl. Numer. Math. 39, No. 3–4, 349–365 (2001; Zbl 0996.65073)] and the advantages of the novel BLieDF integrator are shown.
MSC:
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Citations:
Zbl 0996.65073Software:
RODASReferences:
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