论文标题
$ \ mathbb {r}^3 $中的圆锥系统的空形式由其对称性确定
Null-forms of conic systems in $\mathbb{R}^3$ are determined by their symmetries
论文作者
论文摘要
我们解决了圆锥$ 3 $维系统的无效表征的问题，即控制型系统的可允许速度场在切线空间中形成圆锥（无参数）。这些系统先前已被确定为圆锥非体力学约束或零曲率系统下的最简单控制系统。在这项工作中，我们通过研究无限对称性的谎言代数来直接表征所有控制膜系统中圆锥系统的无效表征。也就是说，我们表明，无限对称性的谎言代数表征了圆锥体系的独特无效形式。
We address the problem of characterisation of null-forms of conic $3$-dimensional systems, that is, control-affine systems whose field of admissible velocities forms a conic (without parameters) in the tangent space. Those systems have been previously identified as the simplest control systems under a conic nonholonomic constraint or as systems of zero curvature. In this work, we propose a direct characterisation of null-forms of conic systems among all control-affine systems by studying the Lie algebra of infinitesimal symmetries. Namely, we show that the Lie algebra of infinitesimal symmetries characterises uniquely null-forms of conic systems.
