On body motion in the upper atmosphere

B.Ya.Lokshin, Yu.M.Okunev, V.A.Sadovnichy, V.A.Samsonov

Institute of mechanics of the Lomonosov MSU

Michurinsky prosp., Moscow, 119192, Russia

The problem of body deceleration in uniform quiescent medium (under action of aerodynamic forces and in absence of forces of other nature) is studied as a typical problem of the theoretical mechanics examining the interference of translation and rotation motions of a body. It is shown that the regime of the rectilinear translation motion for bodies of the irregular shape is, generally speaking, also impossible.

The stability in the simplest particular case of symmetrical body is analyzed and it is shown that the trivial regime is exponentially unstable. In the case of an inhomogeneous sphere there is performed a global analysis of the trajectories of the dynamic system.

In the middle of the XVIII century Euler had formulated and practically solved the model problem on heavy material point motion in the medium with quadratic resistance, thus having started the investigation of various problems of the external ballistics (flight of canon-balls, shells, bullets, etc.). In 1891 Zhukovski added to this model the lift force. It turned out that trajectories of the point motion in this case acquire new shapes and can even resemble trajectories of the bird flight. So the mechanical and mathematical modeling of the flight of bodies with high fineness lifting surfaces began. In 70^th of the last century problems arose related with the returning of modules of spaceships (including unguided ones) that have no wings and thus possess relatively low fineness. In the last time the interest appeared to objects such as meteorites,:. They are shapeless bodies (pieces of ice, stone, metal, etc.) and as a rule have very low fineness. Naturally, when these bodies enter the Earth's or other planet's atmosphere on high speed (over 10 km/sec) many of them are broken in the upper atmosphere. But some fragments continue their flight and even reach the Earth's surface. The necessity to estimate the fragments dispersion gives the authors occasion to discuss general properties of motion of bodies having no special form (so to say, bodies of "irregular" shape) in resisting medium.

In the present paper, the problem of body deceleration in uniform quiescent medium (under action of aerodynamic forces and in absence of forces of other nature) is studied as a typical problem of the theoretical mechanics examining the interference of translation and rotational motions of a body.