Special Session
59 
Central configurations, periodic solutions, variational method and beyond in celestial mechanics 
Organizer(s): 



Introduction:

This special session will concentrate on the latest developments in the field of celestial mechanics. In classical celestial mechanics, the motion of the planets and stars is governed by universal gravity and it is mathematically formulated as a secondorder system of differential equations, known as the Nbody problem. One of the most important types of solutions to the Nbody problem is periodic in nature. Among this class of solutions, analyzing the structure and stability of simple, rigidly rotating orbits known as relative equilibria (or central configurations) leads to a greater understanding of the complexities in the full problem.
The study of the Nbody problem continues to attract researchers in a wide range of fields including dynamical systems, topology, variational methods, algebraic geometry and numerical methods. Much progress has been made recently in the study of the finiteness and stability questions in the Nbody problem. This special session provides a marketplace for ideas, and helps identify trends and areas of new opportunity in the field. The session brings established researchers and recent Ph. D graduates together, some of whom are women or from groups underrepresented in mathematics. Some specific topics to be covered include central configurations, discovery of new periodic solutions, variational methods, regularization of collisions, absence of collisions, stability of periodic solutions, spacecraft orbital design and applications of Morse index and Maslov index to the Nbody problem. If the schedule permits, we anticipate ending the session with a discussion on open problems. 


