From Chaplygin Sleigh to Torpedo: An~example of a~Cartan-Geometric View of Left-Invariant Nonholonomic Systems

Pavla Musilova; Jan Slovak

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arXiv · 2610.26439

From Chaplygin Sleigh to Torpedo: An~example of a~Cartan-Geometric View of Left-Invariant Nonholonomic Systems

Pavla Musilova·Jan Slovak

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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 $\mathfrak{se}(3)$.

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Pavla Musilova, Jan Slovak. 2026-10-19. From Chaplygin Sleigh to Torpedo: An~example of a~Cartan-Geometric View of Left-Invariant Nonholonomic Systems. https://arxiv.org/abs/2610.26439

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