Numerical Integrators for Mechanical Systems on Lie Groups
Viyom Vivek, David Martin de Diego, Ravi N Banavar
众所周知,回缩图是所有数值集成体的种子。 这些基于回缩图的集成器可以进一步提升为切线和共聚的紧密连接,从而产生机械系统的结构保护集成器。 我们探索我们的机械系统的配置空间是具有某些对称性的Lie组的特殊情况。 在这里,集成器根据Lie组的切线和共通包可琐碎的特性进行了简化。 最后,我们提出了一个框架,用于设计Euller-Poincare和Lie-Poisson类型方程的数值集成器。
Retraction maps are known to be the seed for all numerical integrators. These retraction maps-based integrators can be further lifted to tangent and cotangent bundles, giving rise to structure-preserving integrators for mechanical systems. We explore the particular case where the configuration space of our mechanical system is a Lie group with certain symmetries. Here, the integrator simplifies based on the property that the tangent and cotangent bundles of Lie groups are trivializable. Finally,...