Conservative and Dissipative Models of Celestial Mechanics

This book is devoted to the presentation and discussion of some models of relevance in Celestial Mechanics and Astrodynamics. The motions of celestial bodies, either natural or artificial, are governed by conservative forces, like the gravitational attraction that preserve the total energy and by dissipative forces, like the tidal torque, Stokes drag, and the Poynting-Robertson effect. The basic idea of this book is to describe in each chapter a model in the conservative setting, providing its main features, and then to extend the model by including dissipative forces. In fact, the dynamics of many objects of the Solar system is well described, in a first approximation, by a conservative model; however, in the long term, dissipative effects may play a relevant role, for example, in shaping the dynamics and affecting the evolutionary history of the Solar system.

Motivated by this observation, in this book, different models are presented and their main features are described in the conservative setting, but dissipative contributions, pertinent to the model, are added as well, which may lead to a completely different dynamics on long time scales. Conservative systems have a larger variety of motions, e.g., the dynamics can take place on rotational tori, librational motions, periodic orbits, and chaotic trajectories. On the contrary, dissipative systems admit a less rich dynamics, since the dissipation forces the motion to take place on a few attractors, e.g., rotational tori, periodic orbits or strange attractors. Besides, dissipative systems often need extra parameters to compensate for the loss of energy and to allow the dynamics to take place on non-trivial attractors.

The book is addressed to graduate students and researchers interested in models of Celestial Mechanics and Astrodynamics.

Provides an explicit presentation of several different models in Celestial Mechanics Offers a comprehensive overview of various problems in Celestial Mechanics and Astrodynamics Presents models in the conservative setting and also in the dissipative framework

Autorentext

Alessandra Celletti received her PhD in 1989 at the Swiss Federal Institute of Technology in Zurich (ETH) under the supervision of Professors Jurgen Moser and Jorge Waldvogel. She is a full professor of Mathematical Physics at the University of Rome Tor Vergata and since 2020, she has been a member of the governing board and the Vice President of ANVUR. Her research interests include Celestial Mechanics and Dynamical Systems with reference to perturbative methods and applications to Solar system dynamics. She is a founding member of the Italian Society of Celestial Mechanics and Astrodynamics that chaired from 2001 to 2013. Since 2010, she has been an honorary member of the "Celestial Mechanics Institute". In 2018, she became the President of the Scientific Committee in Celestial Mechanics of the IAU and in 2019-2020, she was in the Governing Board of the Italian Space Agency. In 2023, she was awarded the "Dirk Brouwer Career Award" from the American Astronomical Society. In addition, the asteroid 117539 bears her name.

Inhalt

Chapter 1. Conservative and dissipative dynamical systems.- Chapter 2. Perturbation theory.- Chapter 3. Kepler's problem.- Chapter 4. The 3-body problem. Chapter 5. Euler-Lagrange solutions.- Chapter 6. Halo orbits.- Chapter 7. Laplace resonance.- Chapter 8. The geopotential and the J2 problem.- Chapter 9. Earth's satellite and space debris dynamics.- Chapter 10. The spin-orbit problem.- Chapter 11. Rotational dynamics with obliquity.- Chapter 12. The spin-spin model.- Chapter 13. Dumbbell and tether models.- Chapter 14. Solar sails.