Keplerian orbits and their properties

November 19-23, 2007

3 op/1.5 ov

lectures 16 hours

demonstrations 4 hours

home assignments

examination

Lecturer: Professor Konstantin V. Kholshevnikov

Academician of RAEN, DSc, chair in Celestial mechanics, St. Petersburg State University

Course description:

After discovery of a vast class of Solar system bodies that have close approaches with planets (in particular, with the Earth), a question of topology and metrics of orbital space becomes actual. We succeeded in solving the problem under the condition of unperturbed motion constructing different metrics in spaces of Keplerian orbits. It turned out that it is reasonable to construct at least two different orbital spaces (space of all orbits and space of curvilinear orbits). A distance between orbits as sets in the configuration space serves as an important functional in these spaces.

Program of the course:

1. Different definitions of "orbit"; spaces of unperturbed (Keplerian) orbits

2. Metrics in spaces of Keplerian orbits

3. Topology in spaces of Keplerian orbits

4. Linking coefficient of a pair of orbits

5. Distance between orbits as sets embedded in 3-dimensional space

Model and real problems of determining different distances in spaces of orbits are solved on demonstrations.

Registration and further information:

by e-mail: alemio@utu.fi

Hamiltonian mechanics and search of

periodic orbits in N-Body-Problem

November 26-30, 2007

3 op/1.5 ov

lectures 16 hours

demonstrations 4 hours

home assignments

examination

Lecturer: Associate Professor Vladimir B. Titov, PhD, Docent,

Chair of Celestial mechanics, St. Petersburg State University

Course description:

Hamilton's principle provides a new and equivalent to Lagrangian mechanics way of looking at classical mechanics. These equations provide deeper insights into the general structure of classical, as well as its connection to other areas of science. Using the Hamilton's principle, several new classes of periodic orbits were constructed in N-Body-Problem. Symmetries of the system turned out to be useful for finding these periodic solutions.

Registration and further information:

by e-mail: alemio@utu.fi