论文标题
通过非单学力学的同质空间上拉格朗日系统的高级集成商
High-order integrators for Lagrangian systems on homogeneous spaces via nonholonomic mechanics
论文作者
论文摘要
在本文中，均质空间上的高阶数值集成符将作为非统一分区runge-kutta munthe-kaas（RKMK）方法的应用。 同质空间$ m $是一个$ g $传统作用的多种多样。这样的空间可以理解为商的$ m \ cong g/h $，其中$ h $一个封闭的谎言子组是$ m $的每个点的各向同性组。 $ g $的谎言代数可能被分解为$ \ mathfrak {g} = \ mathfrak {m} \ oplus \ mathfrak {h} $，其中$ \ mathfrak {h h} $是产生$ h $ and $ h $ and $ \ mathfrak的subalgebra。因此，$ m $上的变异问题可以通过要求在$ \ mathfrak {m} $上保留在$ g $上的非语言限制问题。 非语言分区的RKMK集成剂的得出是对谎言组的离散变异原理获得的修改，并且可以解释为遵守离散的Chetaev原理。这些集成商倾向于保留其纯粹的变异对应物的几种特性。
In this paper, high-order numerical integrators on homogeneous spaces will be presented as an application of nonholonomic partitioned Runge-Kutta Munthe-Kaas (RKMK) methods on Lie groups. A homogeneous space $M$ is a manifold where a group $G$ acts transitively. Such a space can be understood as a quotient $M \cong G/H$, where $H$ a closed Lie subgroup, is the isotropy group of each point of $M$. The Lie algebra of $G$ may be decomposed into $\mathfrak{g} = \mathfrak{m} \oplus \mathfrak{h}$, where $\mathfrak{h}$ is the subalgebra that generates $H$ and $\mathfrak{m}$ is a subspace. Thus, variational problems on $M$ can be treated as nonholonomically constrained problems on $G$, by requiring variations to remain on $\mathfrak{m}$. Nonholonomic partitioned RKMK integrators are derived as a modification of those obtained by a discrete variational principle on Lie groups, and can be interpreted as obeying a discrete Chetaev principle. These integrators tend to preserve several properties of their purely variational counterparts.
