A generalization of the Suslov problem with changing parameters is considered. The physical interpretation is a Chaplygin sleigh moving on a sphere. The problem is reduced to the study of a two-dimensional system describing the evolution of the angular velocity of a body. The system without viscous friction and the system with viscous friction are considered. Poincaré maps are constructed, attractors and noncompact attracting trajectories are found. The presence of noncompact trajectories in the Poincaré map suggests that acceleration is possible in this nonholonomic system. In the case of a system with viscous friction, a chart of dynamical regimes and a bifurcation tree are constructed to analyze the transition to chaos. The classical scenario of transition to chaos through a cascade of period doubling is shown, which may indicate attractors of Feigenbaum type.

中文翻译：

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两个非完整混沌系统。第一部分：关于Suslov问题

考虑参数变化的Suslov问题的推广。物理解释是在球体上移动的Chaplygin雪橇。该问题被简化为研究二维系统的研究，该系统描述了物体的角速度的演变。考虑没有粘滞摩擦的系统和有粘滞摩擦的系统。构造庞加莱地图，找到吸引子和非紧凑的吸引轨迹。庞加莱图中非紧凑轨迹的存在表明，在这种非完整系统中可能进行加速。在具有粘滞摩擦的系统中，构造了动态状态图和分叉树来分析向混沌的过渡。显示了通过一倍周期倍增过渡到混沌的经典场景，