Proceedings of the Third Alexander von Humboldt Colloquium on Celestial Mechanics

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.

All magnetized planets in our solar system (Mercury, Earth, Jupiter, Saturn, Uranus, and Neptune) interact strongly with the solar wind and possess well developed magnetotails. It is not only the strongly magnetized planets that have magnetotails. Mars and Venus have no global intrinsic magnetic field, yet they possess induced magnetotails. Comets have magnetotails that are formed by the draping of the interplanetary magnetic field. In the case of planetary satellites (moons), the magnetotail refers to the wake region behind the satellite in the flow of either the solar wind or the magnetosphere of its parent planet. The largest magnetotail of all in our solar system is the heliotail, the “magnetotail” of the heliosphere. The variety of solar wind conditions, planetary rotation rates, ionospheric conductivity, and physical dimensions provide an outstanding opportunity to extend our understanding of the influence of these factors on magnetotail processes and structures. Volume highlights include: Discussion on why a magnetotail is a fundamental problem of magnetospheric physics Unique collection of tutorials on a large range of magnetotails in our solar system In-depth reviews comparing magnetotail processes at Earth with other magnetotail structures found throughout the heliosphere Collectively, Magnetotails in the Solar System brings together for the first time in one book a collection of tutorials and current developments addressing different types of magnetotails. As a result, this book should appeal to a broad community of space scientists, and it should also be of interest to astronomers who are looking at tail-like structures beyond our solar system.

It is now a well established tradition that every four years, at the end of winter, a group of "celestial mechanicians" from all over the world gather at the "Alpen gasthof Peter Rosegger" in the Styrian Alps (Ramsau, Austria). This time the colloquium was held from March 17 to March 23, 1996 and was devoted to the Dynamical Behaviour of our Planetary System. The papers covered a large range of questions of current interest: theoretical questions (re- nances, universal properties, non integrability, transport, ... ) and questions about numerical tools ( symplectic maps, indicators of chaos, ... ) were particularly well represented; the never ending problem of the sculpting of the asteroid belt was also qui te popular. You will find in the following pages a pot-pourri of what we listen to; you will miss of course the diversity of accents with which the tunes were delivered: from China, from Japan, from Brazil, from the United-States of America and from all over Europe, East and West. Let us not forget that the comet 199682 (Hyakutake) came to visit us; many an evening was spent on the deck of the Alpengasthof contemplating this celestial visitor who liked to play hide-and-seek behind the spruce trees.

This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.

IAU Transactions are published as a volume corresponding to each General Assembly. Volume A is produced prior to the Assembly and contains Reports on Astronomy, prepared by each Commission President. The intention is to summarize the astronomical results that have affected the work of the Commission since the production of the previous Reports up to a time which is about one year prior to the General Assembly. Volume B is produced after the Assembly and contains accounts of Commission Meetings which were held, together with other material. The reports included in the present volume range from outline summaries to lengthy compilations and references. Most reports are in English.