H. R. Dullin, “Poisson integrator for symmetric rigid bodies”, Regul. Chaotic Dyn., 9:3 (2004), 255

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Regular and Chaotic Dynamics, 2004, Volume 9, Issue 3, Pages 255–264
DOI: https://doi.org/10.1070/RD2004v009n03ABEH000279 (Mi rcd745)

This article is cited in 17 scientific papers (total in 17 papers)

Effective computations in modern dynamics

Poisson integrator for symmetric rigid bodies

H. R. Dullin

Department of Mathematical Sciences, Loughborough University, LE11 3TU, UK

Citations (17)

DOI: https://doi.org/10.1070/RD2004v009n03ABEH000279

Abstract: We derive an explicit second order reversible Poisson integrator for symmetric rigid bodies in space (i.e. without a fixed point). The integrator is obtained by applying a splitting method to the Hamiltonian after reduction by the

$S^1$ body symmetry. In the particular case of a magnetic top in an axisymmetric magnetic field (i.e. the Levitron) this integrator preserves the two momentum integrals. The method is used to calculate the complicated boundary of stability near a linearly stable relative equilibrium of the Levitron with indefinite Hamiltonian.

Received: 30.09.2004

Bibliographic databases:

Document Type: Article

MSC: 70E15, 65P10, 37J25

Language: English

Citation: H. R. Dullin, “Poisson integrator for symmetric rigid bodies”, Regul. Chaotic Dyn., 9:3 (2004), 255–264

Citation in format AMSBIB

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\by H. R. Dullin

\paper Poisson integrator for symmetric rigid bodies

\jour Regul. Chaotic Dyn.

\yr 2004

\vol 9

\issue 3

\pages 255--264

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\crossref{https://doi.org/10.1070/RD2004v009n03ABEH000279}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2104171}

\zmath{https://zbmath.org/?q=an:1102.70004}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004RCD.....9..255D}

Linking options:

https://www.mathnet.ru/eng/rcd745

https://www.mathnet.ru/eng/rcd/v9/i3/p255

This publication is cited in the following 17 articles:

Sean R. Dawson, Holger R. Dullin, Diana M.H. Nguyen, “The Harmonic Lagrange Top and the Confluent Heun Equation”, Regul. Chaotic Dyn., 27:4 (2022), 443–459
S. I. Zub, S. S. Zub, V. S. Lyashko, N. I. Lyashko, S. I. Lyashko, “Mathematical Model of Interaction of a Symmetric Top with an Axially Symmetric External Field”, Cybern Syst Anal, 53:3 (2017), 333
Juergen Geiser, Multicomponent and Multiscale Systems, 2016, 153
S.I. Lyashko, S.I. Zub, S.S. Zub, N.I. Lyashko, A.Yu. Chernyavskiy, “Grid and cloud computing for the modeling of the motion of a magnetized assymmetric body in an external magnetic field”, Dopov. Nac. akad. nauk Ukr., 2016, no. 9, 29
Alexandre C. M. Correia, “Cassini states for black hole binaries”, Monthly Notices of the Royal Astronomical Society: Letters, 457:1 (2016), L49
Jürgen Geiser, Karl Felix Lüskow, Ralf Schneider, Lecture Notes in Computer Science, 9045, Finite Difference Methods,Theory and Applications, 2015, 193
Alexandre C. M. Correia, “Stellar and planetary Cassini states”, A&A, 582 (2015), A69
Stanislav S. Zub, “Stable orbital motion of magnetic dipole in the field of permanent magnets”, Physica D: Nonlinear Phenomena, 275 (2014), 67
Lyudmila Grigoryeva, Juan-Pablo Ortega, Stanislav S. Zub, “Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies”, Journal of Geometric Mechanics, 6:3 (2014), 373
Jürgen Geiser, Karl Felix Lüskow, Ralf Schneider, “Levitron: multi-scale analysis of stability”, Dynamical Systems, 29:2 (2014), 208
Holger R. Dullin, “Semi-global symplectic invariants of the spherical pendulum”, Journal of Differential Equations, 254:7 (2013), 2942
Jürgen Geiser, “Multiscale methods for levitron problems: Theory and applications”, Computers & Structures, 122 (2013), 27
Benoît Noyelles, “Expression of Cassini's third law for Callisto, and theory of its rotation”, Icarus, 202:1 (2009), 225
Roman Kozlov, “High-order conservative discretizations for some cases of the rigid body motion”, Physics Letters A, 373:1 (2008), 23
Keiko M. Aoki, “Symplectic Integrators Designed for Simulating Soft Matter”, J. Phys. Soc. Jpn., 77:4 (2008), 044003
Phani Kumar V. V. Nukala, William Shelton Jr, “Semi‐implicit reversible algorithms for rigid body rotational dynamics”, Numerical Meth Engineering, 69:12 (2007), 2636
G. Boué, J. Laskar, “Precession of a planet with a satellite”, Icarus, 185:2 (2006), 312

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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