![\begin{displaymath}\begin{array}[t]{lll}
\frac{d\Omega}{d\alpha} dt = d\lamb...
...t =-d\beta, &\frac{d\Omega}{d\nu} dt =-d\gamma,
\end{array}\end{displaymath}](citation/img2.png)
Recently there have been significant mathematical breakthroughs in Celestial Mechanics, concerning difficult problems: always more precise numerical evidence of the instability of the solar system, more complete classification of relative equilibrium configurations, discovery of new quasiperiodic or periodic orbits with new kinds of symmetries, new results on non-integrability, sharper results from averaging methods and KAM theory.
As the 200th anniversary of two remarkable Mémoires of Poisson and Lagrange on the Hamiltonian aspects of the method of the variation of constants approaches (see more details below), a national workshop will be held in Paris in December 2007 on mathematical aspects of Celestial Mechanics. It will focus on averaging as well as on KAM and weak KAM theories, with a view to their consequences in the n-body problem.
In December 2007, we will be commemorating the forthcoming 200th anniversary of two remarkable Mémoires of Poisson and Lagrange on the Hamiltonian aspects of the method of the variation of constants.
« [...] Poisson was twenty-seven when he presented this superb work at the Académie. Towards the end of 1808, a completely unexpected event took by surprise the scientific community, who was immediately enthusiastic. Lagrange had been resting for a long time, enjoying his glory. He would attend all sessions assiduously, but without uttering a single word [...] Suddenly, Lagrange wakes up, and his awakening is that of a lion. On August 17 1808 at the Bureau des Longitudes and the next Monday 22 at the Académie des Sciences, he reads one of the most admirable Mémoires ever written by a mathematician. The work was entitled Mémoire on the theory of variations of elements of planets, and in particular of variations of the major axes of their orbits. » (F. Arago, Œuvres complètes, 1854, p. 654)
« In Astronomy, elements of a planet refer to those quantities which determine its orbit around the Sun, supposedly an ellipse, as well as to the location of the planet at a given time, which is called the epoch. There are five of these quantities, two of which, the major axis or the mean distance which is half of it, and the eccentricity, determine the size of the ellipse, with the Sun located at one of its foci; the other three, the longitude of the aphelion, that of the node and the inclination, determine the position of the major axis in the plane of the ellipse and the position of this plane on a plane which is thought of as fixed with respect to stars. If these five quantities together with the epoch are known for a planet, one can find its location in the sky at all times, using these two laws discovered by Kepler according to which the area swept in the ellipse by the position vector grows linearly with to time, and the time of revolution is proportional to the square root of the cube of the major axis. [...]
During the last century [...], it was established that the motion of a planet attracted by the Sun proportionally to the inverse of their distance squared, depends on three differential equations of the second order, which consequently require six integrations; each of these integrations introduces an arbitrary constant in the computation; so that in the last analysis the solution of the Problem depends on six arbitrary constants, and these are the elements themselves of the planet, or functions of these elements.
However, not only are the planets attracted by the Sun, but also they attract each other, and the effect of this mutual action is to disturb their elliptic motion and to produce inequalities which are called perturbations, the computation of which is long and subtle and has since Newton been a subject of research of Geometers concerned with the Theory of the System of the World. » ([L1], p. 713)
Also see P. Bernard's course this Fall on weak KAM theory.
albouy at
imcce.frpbernard at ceremade.dauphine.frfejoz at math.jussieu.frmarco
at math.jussieu.frlaurent at imcce.frsauzin at
imcce.frCourses and talks will take place in Amphi Darboux of Institut Henri Poincaré.
Grants do not allow to pay for the travel and living expenses of participants. This is why we call the workshop national. On the other hand the organizing committe will heartfully help participants to find a place for lodging in Paris, or send formal invitations.
Participants staying over two weeks will generally rather stay in one of the following residences:
Short term participants will rather stay in a hotel. This is a list; all of them are located close to IHP (choice of IHP). We advertise the following two hotels, which are particularly not expansive, but well located and clean :
IHP also gives a choice of appartments to rent, of student rooms and hotels.