Abstract

In the paper, the dynamics is investigated of an uncontrolled multi-link wheeled vehicle consisting of trolleys with one wheel pair that are attached to the previous link with metal frames and are capable of rotating around their anchor points. The mechanical system under consideration is nonholonomic, since it has additional nonholonmic kinamic connections. A system of differential equations is obtained that describes the dynamics of motion of this wheeled vehicle using the joint solution of the equations of motion in the Lagrange form with indefinite factors and time derivatives of nonholonomic equations of constraints. The cases of constant and variable location of the center of mass of the leading link are investigated. In the case of a constant location of the center of mass of the leading link, the problem is reduced to the system reduced to the level of the integral of the kinetic energy of the system. The stability of the systems thus obtained is analyzed, and the graphs of the desired functions and phase portraits are constructed.

中文翻译：

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多连杆非受控轮式车辆的动力学

摘要

在本文中，研究了一种不受控制的多连杆轮式车辆的动力学，该轮式车辆由带有一对车轮的小车组成，这些小车与一对前轮通过金属框架相连，并能够围绕其锚点旋转。所考虑的机械系统是非完整的，因为它具有其他非完整的动力学连接。获得了一个微分方程系统，该系统使用具有不确定因素和非完整约束方程的时间导数的拉格朗日形式的运动方程的联合解，描述了该轮式车辆的运动动力学。研究了导向连杆的质心位置恒定和可变的情况。如果前导杆的质心位置恒定，问题减少到系统减少到系统动能积分的程度。分析由此获得的系统的稳定性，并构建所需功能的图形和相图。