BDF integrators for constrained mechanical systems on Lie groups
BDF integrators for constrained mechanical systems on Lie groups
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李群约束机械系统的 BDF 积分器
DOI：
10.1016/j.cam.2019.112517
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
M. Arnold
中科院分区：
文献类型：
--
作者：
Victoria Wieloch;M. Arnold
BDF类型的多步法是几种工业多体系统仿真软件中的选择方法。在本文中，BDF被应用到约束系统的非线性配置空间与李群结构，允许，例如，一个表示的多体系统与大旋转没有奇点。k步李群积分器BLieDF避免了通过指数映射的略微扰动的参数来表示配置空间中的数值流的非线性而无需任何耗时的重新参数化的降阶。将该积分器与Faltinsen，Marthinsen和Munthe-Kaas（2001）提出的李群多步法进行了比较，显示了新BLieDF积分器的优点.
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, eg, 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 Faltinsen, Marthinsen and Munthe-Kaas (2001) and the advantages of the novel BLieDF integrator are shown.