论文标题
两步免费的谎言组
Co-adjoint orbits and time-optimal problems for two-step free-nilpotent Lie groups
论文作者
论文摘要
我们描述了两步游离尼尔替代代数的共同伴侣轨道和CASIMIR功能。符号叶面由不同维度的lie calgebra的仿射子空间组成。 此外，我们考虑了两步carnot组上的剩余时间最佳问题，为此，一组可允许的速度是一个严格的凸层compactum，这是谎言代数的第一层中包含其内部起源的lie代数。我们描述了哈密顿制度最大原理的垂直子系统的积分。此外，我们描述了该子系统和控制的解决方案的恒定性和周期性，并为二维共同辅助轨道表征其流量。
We describe co-adjoint orbits and Casimir functions for two-step free-nilpotent Lie algebras. The symplectic foliation consists of affine subspaces of the Lie coalgebra of different dimensions. Further, we consider left-invariant time-optimal problems on two-step Carnot groups, for which the set of admissible velocities is a strictly convex compactum in the first layer of the Lie algebra containing the origin in its interior. We describe integrals for the vertical subsystem of the Hamiltonian system of Pontryagin maximum principle. Further, we describe constancy and periodicity of solutions to this subsystem and controls, and characterize its flow, for two-dimensional co-adjoint orbits.
