Recent Advances in Celestial and Space Mechanics

1. Front Matter

   Pages i-ix

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2. Integrability and Non Integrability of Some n Body Problems

   • Thierry Combot

   Pages 1-30

3. Relative Equilibria in the Full N-Body Problem with Applications to the Equal Mass Problem

   • Daniel J. Scheeres

   Pages 31-81

4. Station Keeping Strategies for a Solar Sail in the Solar System

   • Ariadna Farrés, Àngel Jorba

   Pages 83-115

5. Minimum Fuel Round Trip from a \(L_2\) Earth-Moon Halo Orbit to Asteroid 2006 RH\(_{120}\)

   • Monique Chyba, Thomas Haberkorn, Robert Jedicke

   Pages 117-142

6. Low-Thrust Transfers Between Libration Point Orbits Without Explicit Use of Manifolds

   • Richard Epenoy

   Pages 143-178

7. Time-Minimum Control of the Restricted Elliptic Three-Body Problem Applied to Space Transfer

   • Monique Chyba, Geoff Patterson, Gautier Picot

   Pages 179-208

8. On Local Optima in Minimum Time Control of the Restricted Three-Body Problem

   • Jean-Baptiste Caillau, Ariadna Farrés

   Pages 209-302

This book presents recent advances in space and celestial mechanics, with a focus on the N-body problem and astrodynamics, and explores the development and application of computational techniques in both areas. It highlights the design of space transfers with various modes of propulsion, like solar sailing and low-thrust transfers between libration point orbits, as well as a broad range of targets and applications, like rendezvous with near Earth objects. Additionally, it includes contributions on the non-integrability properties of the collinear three- and four-body problem, and on general conditions for the existence of stable, minimum energy configurations in the full N-body problem.
A valuable resource for physicists and mathematicians with research interests in celestial mechanics, astrodynamics and optimal control as applied to space transfers, as well as for professionals and companies in the industry.

• Attitude control mechanics
• Low propulsion orbital transfers
• Low-thrust transfers between libration
• Mechanics for vehicles on planetary surfaces
• Optimal control
• Point orbits
• Return missions to mini-Moons
• Solar sailing
• Solar sailing for spacecraft propulsion
• Space mechanics
• Spacecraft propulsion
• Two, three and N-Body dynamics

• Faculte des Sciences Mirande, University of Burgundy, Dijon, France

  Bernard Bonnard

• Department of Mathematics, University of Hawaii, Manoa, Honolulu, USA

  Monique Chyba

Monique Chyba, professor at the University of Hawaii-Manoa, Honolulu, USA, received her Phd in Mathematics from the University of Geneva and the University of Burgundy (1997). Her expertise lies in the development of geometric optimal control methods and its application to real problems especially from physics, biology and engineering. Her contribution varies from robotics, especially optimal guidance and navigation of autonomous underwater vehicles, to applications in the medical field. Her most recent work focuses on designing efficient spacecraft rendezvous mission with temporarily captured orbiters, mathematical modeling of brain morphogenesis based on the distribution of the extracellular matrix structures fractones and the optimization of the protein misfolding cyclic amplification procedure.

Bernard Bonnard, professor at the University of Burgundy and member of the INRIA Team Mc Tao at Sophia Antipolis, France, received his PhD in Mathematics at University of Metz (1978) and completed his Thèse d’ Etat at Grenoble (1983). He is a specialist of geometric optimal control focusing the use of differential geometry, Dynamical systems and Control techniques to analyze optimal control problems and in particular the role of singular trajectories. Other contributions are in sub-Riemannian geometry with applications to the swimming problem at low Reynolds number. His recent domain of applications are space mechanics (attitude control, re-entry shuttle problem, orbital transfer) and control of dissipative quantum systems with applications to MRI (contrast problem).

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