Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the derivation of guiding center dynamics without coordinate
  dependence   The application of conventional guiding-center theory is obstructed by the
global existence problem of coordinates. A general coordinate independent
geometric representation of the guiding center theory is developed, which
clearly defined the procedure for the gyro-averaging and the Lie perturbation
without special coordinates introduced. The unperturbed
Poincar\'e-Cartan-Einstein one-form is calculated to the second-order without
coordinates dependent. To solve the obsession caused by the conventional
guiding-center coordinates, a the Cartesian coordinates implementation of
guiding-center dynamics is presented.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph