Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving two-point boundary value problems using generating functions:
  Theory and Applications to optimal control and the study of Hamiltonian
  dynamical systems   A methodology for solving two-point boundary value problems in phase space
for Hamiltonian systems is presented. Using Hamilton-Jacobi theory in
conjunction with the canonical transformation induced by the phase flow, we
show that the generating functions for this transformation solve any two-point
boundary value problem in phase space. Properties of the generating functions
are exposed, we especially emphasize multiple solutions, singularities,
relations with the state transition matrix and symmetries. Then, we show that
using Hamilton's principal function we are also able to solve two-point
boundary value problems, nevertheless both methodologies have fundamental
differences that we explore. Finally, we present some applications of this
theory. Using the generating functions for the phase flow canonical
transformation we are able to solve the optimal control problem (without an
initial guess), to study phase space structures in Hamiltonian dynamical
systems (periodic orbits, equilibrium points) and classical targeting problems
(this last topic finds its applications in the design of spacecraft formation
trajectories, reconfiguration, formation keeping, etc...).

19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con