Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sub-Riemannian geodesics on the 3-D sphere   The unit sphere $\mathbb S^3$ can be identified with the unitary group SU(2).
Under this identification the unit sphere can be considered as a
non-commutative Lie group. The commutation relations for the vector fields of
the corresponding Lie algebra define a 2-step sub-Riemannian manifold. We study
sub-Riemannian geodesics on this sub-Riemannian manifold making use of the
Hamiltonian formalism and solving the corresponding Hamiltonian system.

3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat