Lie Group Spectral Variational Integrators

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• 作者：James Hall ; Melvin Leok
• 关键词：Symplectic integrators ; Variational integrators ; Lie group integrators ; Geometric numerical integration
• 刊名：Foundations of Computational Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：17
• 期：1
• 页码：199-257
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Numerical Analysis; Economics, general; Applications of Mathematics; Linear and Multilinear Algebras, Matrix Theory; Math Applications in Computer Science; Computer Science, general;
• 出版者：Springer US
• ISSN：1615-3383
• 卷排序：17

文摘

We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic and momentum-preserving, can be constructed to be of arbitrarily high order, or can be made to converge geometrically. Furthermore, these methods are capable of taking very large time-steps. We demonstrate the construction of one such variational integrator for the rigid body and discuss how this construction could be generalized to other related Lie group problems. We close with several numerical examples which demonstrate our claims and discuss further extensions of our work.