论文标题
$（n）$使用极地分解的高阶符号谎言组方法
High-order symplectic Lie group methods on $SO(n)$ using the polar decomposition
论文作者
论文摘要
特殊正交组$ so（n）$的任意高阶的差异集成符是使用极性分解和约束盖金方法构建的。它具有避免在传统谎言组变异方法中产生的指数图的二阶导数的优点。此外，还构建了降低的Lie-lie-lie-lie-lie-lie-lie-lie-lie-lie-lie-lie-lie-liegorithms自然可以通过固定点迭代实现。所提出的方法通过$ SO（3）$上的数值模拟验证，这些模拟表明它们与变量runge-kutta- kutta--nthe-kaas方法在计算效率方面。但是，我们提出的方法更准确地保留了谎言组的结构，并在能量保存附近表现更好。
A variational integrator of arbitrarily high-order on the special orthogonal group $SO(n)$ is constructed using the polar decomposition and the constrained Galerkin method. It has the advantage of avoiding the second-order derivative of the exponential map that arises in traditional Lie group variational methods. In addition, a reduced Lie--Poisson integrator is constructed and the resulting algorithms can naturally be implemented by fixed-point iteration. The proposed methods are validated by numerical simulations on $SO(3)$ which demonstrate that they are comparable to variational Runge--Kutta--Munthe-Kaas methods in terms of computational efficiency. However, the methods we have proposed preserve the Lie group structure much more accurately and and exhibit better near energy preservation.
