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)

Downloads

Issue

Vol. 4 No. 50 (2016)

Section

MATHEMATICAL MODELING OF PROCESSES AND SYSTEMS

License

Authors who publish with this journal agree to the following terms:

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).