Vincent Guibout

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The optimal control of a spacecraft as it transitions between specified states using continuous thrust in a fixed amount of time is studied using a recently developed technique based on Hamilton–Jacobi theory. Started from the first-order necessary conditions for optimality, a Hamiltonian system is derived for the state and adjoints with split boundary(More)
Previous research on the solutions of two-point boundary value problems is applied to spacecraft formation dynamics and design. The underlying idea is to model the motion of a spacecraft formation as a Hamiltonian dynamic system in the vicinity of a reference solution. Then the nonlinear phase flow can be analytically described using generating functions(More)
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent bundles respectively. In particular we show how to obtain a large class of discrete algorithms using this geometric approach.(More)
The optimal control of a spacecraft as it transitions between specified states in a fixed amount of time is studied. We approach the solution to our optimal control problem with a novel technique, treating the resulting system for the state and adjoints as a Hamiltonian system. We show that the optimal control for this system can be found once the F1(More)
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(More)
Periodic orbits are studied using generating functions that yield canonical transformations induced by the phase flow as defined by the Hamilton-Jacobi theory. By posing the problem as a two-point boundary value problem, we are able to develop necessary and sufficient conditions for the existence of periodic orbits of a given period, or going through a(More)
This paper focuses on applications of a general methodology that we developed for solving two-point boundary value problems. Using the Hamilton-Jacobi theory in conjunction with canonical transformation induced by the phase flow, we proved that the generating functions for this transformation solve any two-point boundary value problem in phase space. This(More)
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