Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-order symplectic Lie group methods on $SO(n)$ using the polar
  decomposition   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.

3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys