On the Nonholonomic Routh Sphere in a Magnetic Field

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

In: Regular and Chaotic Dynamics, Vol. 25, No. 1, 01.2020, p. 18-32.

Research output: Contribution to journal › Article › peer-review

Author

Borisov, Alexey V. ; Tsiganov, Andrey V. / On the Nonholonomic Routh Sphere in a Magnetic Field. In: Regular and Chaotic Dynamics. 2020 ; Vol. 25, No. 1. pp. 18-32.

BibTeX

@article{37c8d1c0b41544eda629f00d16f29440,

title = "On the Nonholonomic Routh Sphere in a Magnetic Field",

abstract = "This paper is concerned with the motion of an unbalanced dynamically symmetric sphere rolling without slipping on a plane in the presence of an external magnetic field. It is assumed that the sphere can consist completely or partially of dielectric, ferromagnetic, superconducting and crystalline materials. According to the existing phenomenological theory, the analysis of the sphere{\textquoteright}s dynamics requires in this case taking into account the Lorentz torque, the Barnett-London effect and the Einstein-de Haas effect. Using this mathematical model, we have obtained conditions for the existence of integrals of motion which allow one to reduce integration of the equations of motion to a quadrature similar to the Lagrange quadrature for a heavy rigid body.",

keywords = "37J60, 70F25, 74F15, Barnett-London effect, Einstein-de Haas effect, integrable systems, magnetic field, nonholonomic systems, CHAPLYGIN BALL, MOMENT, MOTION, DYNAMICS",

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

note = "Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd.",

year = "2020",

month = jan,

doi = "10.1134/S1560354720010049",

language = "English",

volume = "25",

pages = "18--32",

journal = "Regular and Chaotic Dynamics",

issn = "1560-3547",

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

number = "1",

}

RIS

TY - JOUR

T1 - On the Nonholonomic Routh Sphere in a Magnetic Field

AU - Borisov, Alexey V.

AU - Tsiganov, Andrey V.

PY - 2020/1

Y1 - 2020/1

N2 - This paper is concerned with the motion of an unbalanced dynamically symmetric sphere rolling without slipping on a plane in the presence of an external magnetic field. It is assumed that the sphere can consist completely or partially of dielectric, ferromagnetic, superconducting and crystalline materials. According to the existing phenomenological theory, the analysis of the sphere’s dynamics requires in this case taking into account the Lorentz torque, the Barnett-London effect and the Einstein-de Haas effect. Using this mathematical model, we have obtained conditions for the existence of integrals of motion which allow one to reduce integration of the equations of motion to a quadrature similar to the Lagrange quadrature for a heavy rigid body.

AB - This paper is concerned with the motion of an unbalanced dynamically symmetric sphere rolling without slipping on a plane in the presence of an external magnetic field. It is assumed that the sphere can consist completely or partially of dielectric, ferromagnetic, superconducting and crystalline materials. According to the existing phenomenological theory, the analysis of the sphere’s dynamics requires in this case taking into account the Lorentz torque, the Barnett-London effect and the Einstein-de Haas effect. Using this mathematical model, we have obtained conditions for the existence of integrals of motion which allow one to reduce integration of the equations of motion to a quadrature similar to the Lagrange quadrature for a heavy rigid body.

KW - 37J60

KW - 70F25

KW - 74F15

KW - Barnett-London effect

KW - Einstein-de Haas effect

KW - integrable systems

KW - magnetic field

KW - nonholonomic systems

KW - CHAPLYGIN BALL

KW - MOMENT

KW - MOTION

KW - DYNAMICS

UR - http://www.scopus.com/inward/record.url?scp=85079644425&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4db94d69-4ab5-37ee-82ff-5a68aa217bee/

U2 - 10.1134/S1560354720010049

DO - 10.1134/S1560354720010049

M3 - Article

AN - SCOPUS:85079644425

VL - 25

SP - 18

EP - 32

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

SN - 1560-3547

IS - 1

ER -

ID: 51917480