The goal of this paper is to extend the notion of Gaussian curvature of two-dimensional surfaces to nonlinear time-optimal control systems in the plane by applying the moving frame method. This notion of curvature was introduced earlier by A. A. Agrachev and R. V. Gamkrelidze by means of Jacobi curves. Here we give a self-contained presentation of its two-dimensional version and apply the results to the well-known Zermelo navigation problem.
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机译：本文的目的是通过应用移动框架方法将二维表面的高斯曲率概念扩展到平面中的非线性时间最优控制系统。 A. A. Agrachev和R. V. Gamkrelidze先前通过Jacobi曲线引入了这种曲率概念。在这里，我们给出了其二维版本的完整介绍，并将结果应用于众所周知的Zermelo导航问题。
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