On the Chaplygin Sphere in a Magnetic Field

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On the Chaplygin Sphere in a Magnetic Field. / Borisov, Alexey V.; Tsiganov, Andrey V.

In: Regular and Chaotic Dynamics, Vol. 24, No. 6, 2019, p. 739-754.

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Author

Borisov, Alexey V. ; Tsiganov, Andrey V. / On the Chaplygin Sphere in a Magnetic Field. In: Regular and Chaotic Dynamics. 2019 ; Vol. 24, No. 6. pp. 739-754.

BibTeX

@article{13ad5d6d0da044b59e31ba40f061b3a0,

title = "On the Chaplygin Sphere in a Magnetic Field",

abstract = "We consider the possibility of using Dirac{\textquoteright}s ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable constraints in the model of a nonholonomic Chaplygin sphere on a plane. We prove that, when a solenoidal field is applied, the general mechanical energy, the invariant measure and the conformally Hamiltonian representation of the equations of motion are preserved. In addition, we consider the case of motion of the nonholonomic Chaplygin sphere in a constant magnetic field taking dielectric and ferromagnetic (superconducting) properties of the sphere into account. As a by-product we also obtain two new integrable cases of the Hamiltonian rigid body dynamics in a constant magnetic field taking the magnetization by rotation effect into account.",

keywords = "37J60, 70F25, 74F15, Barnett — London moment, deformation of Poisson brackets, Grioli problem, magnetic field, nonholonomic mechanics",

author = "Borisov, {Alexey V.} and Tsiganov, {Andrey V.}",

year = "2019",

doi = "10.1134/S156035471906011X",

language = "English",

volume = "24",

pages = "739--754",

journal = "Regular and Chaotic Dynamics",

issn = "1560-3547",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "6",

}

RIS

TY - JOUR

T1 - On the Chaplygin Sphere in a Magnetic Field

AU - Borisov, Alexey V.

AU - Tsiganov, Andrey V.

PY - 2019

Y1 - 2019

N2 - We consider the possibility of using Dirac’s ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable constraints in the model of a nonholonomic Chaplygin sphere on a plane. We prove that, when a solenoidal field is applied, the general mechanical energy, the invariant measure and the conformally Hamiltonian representation of the equations of motion are preserved. In addition, we consider the case of motion of the nonholonomic Chaplygin sphere in a constant magnetic field taking dielectric and ferromagnetic (superconducting) properties of the sphere into account. As a by-product we also obtain two new integrable cases of the Hamiltonian rigid body dynamics in a constant magnetic field taking the magnetization by rotation effect into account.

AB - We consider the possibility of using Dirac’s ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable constraints in the model of a nonholonomic Chaplygin sphere on a plane. We prove that, when a solenoidal field is applied, the general mechanical energy, the invariant measure and the conformally Hamiltonian representation of the equations of motion are preserved. In addition, we consider the case of motion of the nonholonomic Chaplygin sphere in a constant magnetic field taking dielectric and ferromagnetic (superconducting) properties of the sphere into account. As a by-product we also obtain two new integrable cases of the Hamiltonian rigid body dynamics in a constant magnetic field taking the magnetization by rotation effect into account.

KW - 37J60

KW - 70F25

KW - 74F15

KW - Barnett — London moment

KW - deformation of Poisson brackets

KW - Grioli problem

KW - magnetic field

KW - nonholonomic mechanics

UR - http://www.scopus.com/inward/record.url?scp=85076376123&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/chaplygin-sphere-magnetic-field

U2 - 10.1134/S156035471906011X

DO - 10.1134/S156035471906011X

M3 - Article

AN - SCOPUS:85076376123

VL - 24

SP - 739

EP - 754

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

SN - 1560-3547

IS - 6

ER -

ID: 49931981