Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric approach to the optimal control of nonholnomic mechanical
  systems   In this paper, we describe a constrained Lagrangian and Hamiltonian formalism
for the optimal control of nonholonomic mechanical systems. In particular, we
aim to minimize a cost functional, given initial and final conditions where the
controlled dynamics is given by nonholonomic mechanical system. In our paper,
the controlled equations are derived using a basis of vector fields adapted to
the nonholonomic distribution and the Riemannian metric determined by the
kinetic energy. Given a cost function, the optimal control problem is
understood as a constrained problem or equivalently, under some mild regularity
conditions, as a Hamiltonian problem on the cotangent bundle of the
nonholonomic distribution. A suitable Lagrangian submanifold is also shown to
lead to the correct dynamics. We demonstrate our techniques in several examples
including a continuously variable transmission problem and motion planning for
obstacle avoidance problems.

23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th