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PreprintarXiv licencearXiv

The Zhukovskiy-Volterra gyroscope: geometry and reduction

  • Vladimir Dragović
  • Borislav Gajić
  • Božidar Jovanović
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Abstract

We describe a symplectic reduction of the Zhukovskiy integrable case of motion of a rigid body about a fixed point with a gyroscope in ℝn to an integrable magnetic flow on a sphere Sn−1. We also present Zhukovskiy's geometric interpretation of motion of the Euler top with a gyroscope, aka the Zhukovskiy--Volterra gyroscope, and perform a symplectic reduction of this system to an integrable magnetic flow on a $2$-dimensional sphere.

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Cite

BibTeXRIS
BibTeX
@misc{dragovic2026zhukovskiyvolterra,
  title = {{The Zhukovskiy-Volterra gyroscope: geometry and reduction}},
  author = {Vladimir Dragović and Borislav Gajić and Božidar Jovanović},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07789},
  eprint = {2611.07789},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07789},
}
RIS
TY  - UNPB
TI  - The Zhukovskiy-Volterra gyroscope: geometry and reduction
AU  - Vladimir Dragović
AU  - Borislav Gajić
AU  - Božidar Jovanović
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07789
UR  - https://arxiv.org/abs/2611.07789
AB  - We describe a symplectic reduction of the Zhukovskiy integrable case of motion of a rigid body about a fixed point with a gyroscope in ℝ^n to an integrable magnetic flow on a sphere S^n−1. We also present Zhukovskiy's geometric interpretation of motion of the Euler top with a gyroscope, aka the Zhukovskiy--Volterra gyroscope, and perform a symplectic reduction of this system to an integrable magnetic flow on a $2$-dimensional sphere.
ER  -