Abstract

We consider the problem of the time-optimal turning of a system with two degrees of freedom in the form of a material point on a spring oscillating along a rigid weightless rod that rotates in a horizontal plane. The external control moment is applied to the axis of rotation of the rod and is limited in absolute value; and there is no friction. The problem of the fastest turning of the rod through the given angle from a state of rest with oscillation damping is solved. A feature of a nonlinear system is that its linearized model (in the vicinity of the state of rest) is not controllable.

中文翻译：

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弹簧摆的时间最优转动

摘要

我们考虑具有两个自由度的系统的时间最优转动问题，其形式为弹簧上的质点沿着在水平面中旋转的刚性失重杆振荡。外部控制力矩施加在杆的旋转轴上，并且受到绝对值的限制；并且没有摩擦。解决了杆从具有振动阻尼的静止状态最快转动给定角度的问题。非线性系统的一个特征是其线性化模型（在静止状态附近）是不可控的。