Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale invariance and constants of motion   Scale invariance in the theory of classical mechanics can be induced from the
scale invariance of background fields. In this paper we consider the relation
between the scale invariance and the constants of particle motion in a
self-similar spacetime, only in which the symmetry is well-defined and is
generated by a homothetic vector. Relaxing the usual conservation condition by
the Hamiltonian constraint in a particle system, we obtain a conservation law
holding only on the constraint surface in the phase space. By the conservation
law, we characterize constants of motion associated with the scale invariance
not only for massless particles but for massive particles and classify the
condition for the existence of the constants of motion. Furthermore, we find
the explicit form of the constants of motion by solving the conservation
equations.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an