AVDYUSHEV Victor (SCHARM N)

About Me Science Chair Papers Scharm N E-mail

Scientific Work

The Tomsk school of celestial mechanicians is said to be famous for its specialists in numerical methods. I don't account myself such a specialist since I've got no serious paper on this subject. At the same time it doesn't mean that my activity is not connected with the numerical methods. Moreover, quite the contrary, all my activity is impossible without their at all.

F.R. Gantmakher considers analytical mechanics as a section of mechanics where differential equations of motion are derived and also those equations and the methods of integrating them are investigated. In that sense the field of my scientific interests is analytical celestial mechanics but in the aspects of numerical integration.

Differential equations are the core of all simulations of orbital motion. I mean the simulations pretending to practical importance:)) But, as is known, these equations is not integrated exactly, in the form of primitive functions. Recently, for solving them specialists resort to numerical methods of approximate integration with using of computers. Meanwhile, any numerical simulation inevitably connects with the problem of its efficiency.

The efficiency of numerical simulation is characterized by two conceptions: accuracy and speed of integration. Naturally, it depends on 1) what kind of motion equations, 2) what method integrating them and 3) what PC are used. It is clear that the efficiency of simulation can be increased in every of three directions. As is obvious now my direction is the first. In other words, my interest is the transformation of orbital motion equations which enables one to essentially increase the efficiency of numerical integration.

For the whole time I happened to investigate various forms of differential equations mainly applied to simulating asteroid and satellite dynamics. These are regular equations of Kustaanheimo-Stiefel (KS) and Sperling-Burdet (SB); Encke equations (in perturbations): classical ones as well as in KS- and BS-interpretations; equations in various orbital elements and those written in various coordinate frames; Baumgarte's stabilized equations. Some of the main papers on these investigations are in section Papers.

If one try to highlight the range of practical problems I am interested in then it will be all the problems concerning nearplanetary dynamics i.e. the dynamics of artificial and natural satellites as well as the asteroids approaching to major planets. In this direction one of the main results has been the development of the dynamical models of Jovian satellites.

In process of developing the dynamical models of Jovian new and inner satellites, interesting peculiarities in determination of satellite orbits from observations have been revealed. Intensive study of these actually resulted in a list of my interest recently to inverse problems of orbital dynamics.