Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic integrators in the shearing sheet   The shearing sheet is a model dynamical system that is used to study the
small-scale dynamics of astrophysical disks. Numerical simulations of particle
trajectories in the shearing sheet usually employ the leapfrog integrator, but
this integrator performs poorly because of velocity-dependent (Coriolis)
forces. We describe two new integrators for this purpose; both are symplectic,
time-reversible and second-order accurate, and can easily be generalized to
higher orders. Moreover, both integrators are exact when there are no
small-scale forces such as mutual gravitational forces between disk particles.
In numerical experiments these integrators have errors that are often several
orders of magnitude smaller than competing methods. The first of our new
integrators (SEI) is well-suited for disks in which the typical inter-particle
separation is large compared to the particles' Hill radii (e.g., planetary
rings), and the second (SEKI) is designed for disks in which the particles are
on bound orbits or the separation is smaller than the Hill radius (e.g.,
irregular satellites of the giant planets).

20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg