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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Печать: 1064-2315
ISSN Онлайн: 2163-9337

Выпуски:
Том 51, 2019 Том 50, 2018 Том 49, 2017 Том 48, 2016 Том 47, 2015 Том 46, 2014 Том 45, 2013 Том 44, 2012 Том 43, 2011 Том 42, 2010 Том 41, 2009 Том 40, 2008 Том 39, 2007 Том 38, 2006 Том 37, 2005 Том 36, 2004 Том 35, 2003 Том 34, 2002 Том 33, 2001 Том 32, 2000 Том 31, 1999 Том 30, 1998 Том 29, 1997 Том 28, 1996

Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v50.i7.50
pages 48-69

Hamiltonian Dynamics of the Symmetric Top in External Axially-Symmetric Fields. Magnetic Retention of a Rigid Body

Stanislav S. Zub
Kiev National Taras Shevchenko University, Kiev

Краткое описание

The new approach of the study of the dynamic stability of magnetic bodies in external axially-symmetric magnetic fields is proposed. The Hamiltonian describing a wide class of mathematical models of a symmetric top interacting with external axially-symmetric fields and the homogeneous field of gravity force is considered. The method is used for a number of known and new mathematical models.

ЛИТЕРАТУРА

  1. Ortega J.-P., Ratiu T.S., Nonlinear stability of singular relative periodic orbits in Hamiltonian systems with symmetry, J. Geom. Phys., 1999, 32, No. 2, 160–188.

  2. Zub S.I., Zub S.S., Lyashko V.S., Lyashko N.L., Lyashko S.I., Mathematical model of interaction of a symmetric top with an axially symmetric external field, Cybernetics and systems analysis, 2017, 53, No. 3, 333–345.

  3. Grigoryeva L., Ortega J-Р., Zub S., Stability of hamiltonian relative equilibria in symmetric magnetically confined rigid bodies, The J. of Geom. Mech., 2014, No. 6, 373–415.

  4. Zub S.S., Stable orbital motion of magnetic dipole in the field of permanent magnets, Physica D: Nonlinear Phenomena, 2014, 275, 67–73.

  5. Zub S.S., Magnetic levitation in orbitron system, Probl. At. Sci. Technol., 2014, No. 5(93), 31–34.

  6. Zub S.S., Lyashko N.L., Lyashko S.I., Chemiavskyi A.Y., Levitating orbitron: Grid computing, Adv. in Intel. Syst. and Comp., 2018, 754, https://link.springer.com/chapter/10.1007/978-3-319-91008-6_54#citeas.

  7. Lyashko S.I., Nomirovski D.A., Generalized solvability and optimization of parabolic systems in domains with thin weakly permeable inclusions, Cybernetics and systems analysis, 2003, 39, No. 5, 737–745.

  8. Lyashko S.I., Klyushin D.A., Onotskyi V.V., Lyashko N.I., Optimal control of drug delivery from microneedle systems, Ibid., 2018, 54, No. 3, 1–9.

  9. Lyashko S.I., Klyushin D.A., Nomirovsky D.A., Semenov V.V., Identification of age — structured contamination sources in ground water, Optimal control of age — structured populations in economy, demography and the environment, Routledge, London; New Yor.

  10. Lyashko S.I., Semenov V.V., Controllability in classes of singular influences for linear distributed parameter systems, Cybernetics and systems analysis, 2001, No. 1, 18–42.

  11. Lyashko S.I., Nomirovski D.A., Sergienko T.I., Trajectory and final controllability in hyperbolic and pseudohyperbolic systems with generalized actions, Ibid., 2001, No. 5, 157–166.

  12. Zub S.S., Zub S.I., Hamiltonian dynamics of a symmetric top in external fields having axial symmetry. Levitating orbitron, Cornell University, 2015, arXiv:1502.04674, https://arxiv.org/abs/ 1502.04674.


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