The problem of motion of a rigid body with a fixed point in a flow of particles

Authors

  • Alexander S. Kuleshov Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russian Federation
  • Maxim M. Gadzhiev Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2022.315

Abstract

The problem of motion of a rigid body with a fixed point in a free molecular flow of particles is considered. It is shown that the equations of motion of the body generalize the classical Euler - Poisson equations of motion of a heavy rigid body with a fixed point and they are represented in the form of the classical Euler - Poisson equations in the case, when the surface of the body in a flow of particles is a sphere. Problems of the existence of first integrals in the considered system are discussed.

Keywords:

body with a fixed point, free molecular flow, first integrals

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References

Литература

1. Белецкий В.В. Движение искусственного спутника относительно центра масс. Москва, Наука (1965).

2. Баранцев Р.Г., Цжень-юй У. Силы и моменты, действующие на тела вращения в свободномолекулярном потоке. Вестник Ленинградского университета. Серия 1. Математика. Механика. Астрономия, вып. 13, 79-92 (1961).

3. Сазонов В.В. Об одном механизме потери устойчивости режима гравитационной ориентации спутника. Препринт ИПМ № 107. Москва (1988).

4. Рыбникова Т.А., Трещев Д.В. Существование инвариантных торов в задаче о движении спутника с солнечным парусом. Космические исследования 28 (2), 309-312 (1990).

References

1. Beletsky V.V. Dvizhenie iskusstvennogo sputnika otnositel’no centra mass. Moscow, Nauka Publ. (1965). (In Russian) [Eng. transl.: Beletsky V. V. Motion of an Artificial Satellite about its Center of Mass. In Ser.: Mechanics of Space Flight Series. Jerusalem, Israel Program for Scientific Translation (1966)].

2. Barantsev R.G., Tszhen-yui U. Forces and Moments Acting on Solids of Revolution in a Free Molecular Flow. Vestnik of Leningrad University. Series 1. Mathematics. Mechanics. Astronomy, iss. 3, 79-92 (1961). (In Russian)

3. Sazonov V.V. On the framework of loss of stability of the satellite’s gravitational orientation mode. Preprint IPM no. 107. Moscow (1988). (In Russian)

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Published

2022-10-10

How to Cite

Kuleshov, A. S., & Gadzhiev, M. M. (2022). The problem of motion of a rigid body with a fixed point in a flow of particles. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(3), 550–560. https://doi.org/10.21638/spbu01.2022.315

Issue

Section

Mechanics

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