Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second order time dependent tangent bundles and their applications   The aim of this paper is to geometrize time dependent Lagrangian mechanics in
a way that the framework of second order tangent bundles plays an essential
role. To this end, we first introduce the concepts of time dependent
connections and time dependent semisprays on a manifold $M$ and their induced
vector bundle structures on the second order time dependent tangent bundle
$\R\times T^2M$. Then we turn our attention to regular time Lagrangians and
their interaction with $\R\times T^2M$ in different situations such as
mechanical systems with potential fields, external forces and holonomic
constraints. Finally we propose an examples to support our theory.

14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg