Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rattleback: a model of how geometric singularity induces dynamic
  chirality   The rattleback is a boat-shaped top with an asymmetric preference in spin.
Its dynamics can be described by nonlinearly coupled pitching, rolling, and
spinning modes. The chirality, designed into the body as a skewed mass
distribution, manifests itself in the quicker transition of $+$spin
$\rightarrow$ pitch $\rightarrow$ $-$spin than that of $-$spin $\rightarrow$
roll $\rightarrow$ $+$spin. The curious guiding idea of this work is that we
can formulate the dynamics as if a symmetric body were moving in a chiral
space. By elucidating the duality of matter and space in the Hamiltonian
formalism, we attribute asymmetry to space. The rattleback is shown to live in
the space dictated by the Bianchi type ${\rm VI}_{h < -1}$ (belonging to class
B) algebra; this particular algebra is used here for the first time in a
mechanical example. The class B algebra has a singularity that separates the
space (Poisson manifold) into mirror-asymmetric subspaces, breaking the
time-reversal symmetry of nearby orbits.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat