PreprintCC BY 4.0arXiv
From Chaplygin Sleigh to Torpedo: An~example of a~Cartan-Geometric View of Left-Invariant Nonholonomic Systems
Abstract
We discuss two models of a 3D torpedo in which the centre of mass x moves only longitudinally, while the body may rotate about x. Although these are simple examples of left-invariant distributions on the Lie group SE(3), they possess rich geometric structures. For the simplest model, we arrive at an abelian extension of a flat (3,5) path geometry, while adding tiny coupling, we obtain a non-trivial hyperbolic type codimension two CR geometry whose symmetry algebra is just se(3).
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BibTeX
@misc{musilova2026from,
title = {{From Chaplygin Sleigh to Torpedo: An~example of a~Cartan-Geometric View of Left-Invariant Nonholonomic Systems}},
author = {Pavla Musilova and Jan Slovak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26439},
eprint = {2610.26439},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26439},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Chaplygin Sleigh to Torpedo: An~example of a~Cartan-Geometric View of Left-Invariant Nonholonomic Systems
AU - Pavla Musilova
AU - Jan Slovak
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26439
UR - https://arxiv.org/abs/2610.26439
AB - We discuss two models of a 3D torpedo in which the centre of mass x moves only longitudinally, while the body may rotate about x. Although these are simple examples of left-invariant distributions on the Lie group SE(3), they possess rich geometric structures. For the simplest model, we arrive at an abelian extension of a flat (3,5) path geometry, while adding tiny coupling, we obtain a non-trivial hyperbolic type codimension two CR geometry whose symmetry algebra is just se(3).
ER -