Remarks on quadratic Hamiltonians in spaceflight mechanics

Bernard BONNARD; Jean-Baptiste CAILLAU; Romain Dujol

Remarks on quadratic Hamiltonians in spaceflight mechanics

Bernard BONNARD, Jean-Baptiste CAILLAU, Romain Dujol

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter

Abstract

A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.

Original language	English
Title of host publication	Lagrangian and Hamiltonian Methods For Nonlinear Control 2006
Subtitle of host publication	Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, July 2006
Editors	Francesco BULLO, Kenji FUJIMOTO
Publisher	Springer Verlag
Pages	371-379
Number of pages	9
Volume	366
Publication status	Unpublished - 2007

Keywords

Controlled Kepler equation
averaging
quadratic Hamiltonians
Riemannian problems

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http://dujol.perso.enseeiht.fr/research/conferences/LHMNLC2006-Article.pdf

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BONNARD, B., CAILLAU, J-B., & Dujol, R. (2007). Remarks on quadratic Hamiltonians in spaceflight mechanics. Unpublished. In F. BULLO, & K. FUJIMOTO (Eds.), Lagrangian and Hamiltonian Methods For Nonlinear Control 2006: Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, July 2006 (Vol. 366, pp. 371-379). Springer Verlag. http://dujol.perso.enseeiht.fr/research/conferences/LHMNLC2006-Article.pdf

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title = "Remarks on quadratic Hamiltonians in spaceflight mechanics",

abstract = "A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.",

keywords = "Controlled Kepler equation, averaging, quadratic Hamiltonians, Riemannian problems",

author = "Bernard BONNARD and Jean-Baptiste CAILLAU and Romain Dujol",

note = "Publication editors : Francesco BULLO, Kenji FUJIMOTO",

year = "2007",

language = "English",

volume = "366",

pages = "371--379",

editor = "Francesco BULLO and Kenji FUJIMOTO",

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address = "Germany",

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BONNARD, B, CAILLAU, J-B & Dujol, R 2007, Remarks on quadratic Hamiltonians in spaceflight mechanics. in F BULLO & K FUJIMOTO (eds), Lagrangian and Hamiltonian Methods For Nonlinear Control 2006: Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, July 2006. vol. 366, Springer Verlag, pp. 371-379. <http://dujol.perso.enseeiht.fr/research/conferences/LHMNLC2006-Article.pdf>

Remarks on quadratic Hamiltonians in spaceflight mechanics. / BONNARD, Bernard; CAILLAU, Jean-Baptiste; Dujol, Romain.

Lagrangian and Hamiltonian Methods For Nonlinear Control 2006: Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, July 2006. ed. / Francesco BULLO; Kenji FUJIMOTO. Vol. 366 Springer Verlag, 2007. p. 371-379.

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Remarks on quadratic Hamiltonians in spaceflight mechanics

AU - BONNARD, Bernard

AU - CAILLAU, Jean-Baptiste

AU - Dujol, Romain

N1 - Publication editors : Francesco BULLO, Kenji FUJIMOTO

PY - 2007

Y1 - 2007

N2 - A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.

AB - A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.

KW - Controlled Kepler equation

KW - averaging

KW - quadratic Hamiltonians

KW - Riemannian problems

M3 - Chapter

VL - 366

SP - 371

EP - 379

BT - Lagrangian and Hamiltonian Methods For Nonlinear Control 2006

A2 - BULLO, Francesco

A2 - FUJIMOTO, Kenji

PB - Springer Verlag

ER -

Remarks on quadratic Hamiltonians in spaceflight mechanics

Abstract

Keywords

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