Andoyer–deprit variables use to the hess gyroscope phase trajectories exploring

Authors

  • V. V. Kyrychenko National Aviation University

DOI:

https://doi.org/10.18372/1990-5548.50.11397

Keywords:

Gyroscope, rigid body with a fixed point, Hamiltonian, phase portrait, numerical modeling, separatrix, variables Andoyer–Deprit

Abstract

The paper deals with rotation of gyroscope in Hess’ conditions. Motion equations of a solidbody are established on the base of Hamiltonian formalism. There are some analytical researches andcomputer experiments were made on the base of numeral study of phase portrait of equations, which describegyroscope’s motion. The movements of gyroscope, which is submitted to Hess’ conditions in thenull constant of integral of an area and a light weight of the body, are investigated more detailed. Themotion equations and integrals are expressed in variables Andoyer–Deprit. The heteroclinic trajectoriesof the dynamical system are examined by means of the new canonical variables

Author Biography

V. V. Kyrychenko, National Aviation University

Candidate of Science (Phys. & Math). Associate Professor. Aircraft control systems Department

References

W. Hess, Über die Eulerschen Bewegungsgleichun-gen und über eine partikulare Lösung der Bewegung eines Körpers um einen festen Punkt. Math. Ann. 1890. 37, H.2. S. 153–181.

A. V. Borisov and K. V. Yemelyanov, Nonintegra-bility and stochasticity in rigid body dynamics. Izhevsk: Publishing House of Udmurt University Press, 1995, 57 p.

A. V. Borisov and I. S. Mamaev, Rigid body dynamics. Moscow, Izhevsk: R&C Dynamics, 2001, 384 p. (in Russian)

L. Galgani, A. Giorgilli, and J.–M. Strelcyn, “Chaotic motions and transition to stochasticity in the classical problem of the heavy rigid body with a fixed point.” Nuovo Cimento. 1981, 61 B, no. 1, pp. 1–20.

V. V. Kozlov, Methods of qualitative analysis in rigid body dynamics. Izhevsk: R&C Dynamics, 2000, 256 p. (in Russian)

S. L. Ziglin, “Splitting of separatrices, branching of solutions and existence of the integral in rigid body dynamics.” Proceedings of the Moscow Mathema-tical Society. 1980, 41, pp. 287–303.

N. E. Zhukovsky, “Geometric interpretation of the general problem of the motion of a rigid body.” Collected works. Moscow; Leningrad: Gostekhizdat, 1950, vol. 7, pp. 419–425. (in Russian)

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How to Cite

Kyrychenko, V. V. (2016). Andoyer–deprit variables use to the hess gyroscope phase trajectories exploring. Electronics and Control Systems, 4(50), 102–107. https://doi.org/10.18372/1990-5548.50.11397

Issue

Vol. 4 No. 50 (2016)

Section

MATHEMATICAL MODELING OF PROCESSES AND SYSTEMS

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