Gyroscopic Chaplygin Systems and Integrable Magnetic Flows on Spheres

Dragović, Vladimir; Gajić, Borislav; Jovanović, Božidar

doi:10.1007/s00332-023-09901-5

J Nonlinear Sci

2023

DOI: 10.1007/s00332-023-09901-5

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Gyroscopic Chaplygin Systems and Integrable Magnetic Flows on Spheres

Vladimir Dragović

Borislav Gajić

Božidar Jovanović

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2024

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Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation

García-Naranjo,

Marrero,

Martín de Diego

et al. 2024

J Nonlinear Sci

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We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such a term is that the Legendre transformation is an affine, instead of linear, bundle isomorphism between the tangent and cotangent bundles of the configuration space and some care is needed in the development of the geometric formalism. At the end of the day, the affine nature of the Legendre transform is reflected in the affine dependence of the brackets that we construct on the momentum variables. Our study is motivated by a wide class of nonholonomic systems involving rigid bodies with internal rotors which are of interest in control. Our construction provides a natural geometric framework for the (known) Hamiltonisations of the gyrostatic generalisations of the Suslov and Chaplygin sphere problems.

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Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation

García-Naranjo,

Marrero,

Martín de Diego

et al. 2024

J Nonlinear Sci

View full text Add to dashboard Cite

show abstract

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Gyroscopic Chaplygin Systems and Integrable Magnetic Flows on Spheres

Cited by 1 publication

References 52 publications

Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation

Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation

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