Collective symplectic integrators
Collective symplectic integrators
复制标题
集体辛积分器
DOI：
10.1088/0951-7715/27/6/1525
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发表时间：
2013
期刊：
影响因子：
1.7
通讯作者：
Olivier Verdier
中科院分区：
文献类型：
--
作者：
R. McLachlan;K. Modin;Olivier Verdier
我们构造了李泊松系统的辛积分器。积分器是标准的辛（分）龙格-库塔方法。它们的相空间是一个具有动量映射J的哈密顿作用的辛向量空间，其范围是目标李泊松流形，它们的哈密顿量是集合的，即是J拉回的目标哈密顿量。该方法给出了对任意哈密顿量用4个变量表示的辛中点规则。该方法专门研究了一个足够大的对称群作用于J的纤维的情况，并推广到向量空间携带分岔的情况。给出了涉及许多经典群的例子。
We construct symplectic integrators for Lie–Poisson systems. The integrators are standard symplectic (partitioned) Runge–Kutta methods. Their phase space is a symplectic vector space equipped with a Hamiltonian action with momentum map J whose range is the target Lie–Poisson manifold, and their Hamiltonian is collective, that is, it is the target Hamiltonian pulled back by J. The method yields, for example, a symplectic midpoint rule expressed in 4 variables for arbitrary Hamiltonians on . The method specializes in the case that a sufficiently large symmetry group acts on the fibres of J, and generalizes to the case that the vector space carries a bifoliation. Examples involving many classical groups are presented.