Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational principles for conformal geodesics   Conformal geodesics are solutions to a system of third order of equations,
which makes a Lagrangian formulation problematic. We show how enlarging the
class of allowed variations leads to a variational formulation for this system
with a third--order conformally invariant Lagrangian. We also discuss the
conformally invariant system of fourth order ODEs arising from this Lagrangian,
and show that some of its integral curves are spirals.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics