Dynamics of extended celestial bodies and rings. Papers based on the presentations at the thematic winter school of astronomy, Lanslevillard, France, March 2003.
This book is devoted to the study of the dynamics of celestial bodies, in cases where they cannot be approximated by material points. The book starts with a tutorial article by Tokieda on the fundamentals of the rigid body dynamics, where the inertia matrix is introduced, several examples are provided, Euler equations are derived and Euler, Lagrange and Kovalevskaya tops are studied. The article by Legros, Greff and Tokieda deals with viscoelastic deformations of Earth and with the problem of rotation of a deformable planet, while the contribution by Deleflie and Exertier presents a review on the determination of gravitational fields of extended bodies with an application to the Earth's gravitational field. Hestroffer and Tanga discuss the derivation of the rotational state of asteroids from observational data. In the article by Michel, results on asteroid collisions are presented, based on laboratory experiments and numerical simulations, reproducing the main properties of asteroid families, while Valsecchi presents a modification of Öpic's theory of planetary close encounters, allowing the study of such encounters far from the nodes of the orbit of the small body. An analysis of the Cassini's state in the case of the Moon by a simplified model is presented in Henrard's review. D'Hoedt and Lemaitre apply to the study of 3:2 spin-orbit resonance of Mercury a two-degree-of-freedom model. The volume concludes with a review by Sicardy on the planetary ring dynamics with emphasis on their flattening, thickness and resonant interactions with satellites. In conclusion, this volume may serve well as a basic tutorial for the study of the title problem for extended bodies of our Solar system.
scientific article