自由轴对称变质量系统的运动几何和章动稳定性
Geometry of motion and nutation stability of free axisymmetric variable mass systems
摘要：
在经典力学中，“运动几何学”指的是将自由旋转物体的运动形象化的发展。本文发展了一种研究轴对称变质量系统转动运动的方法。这种方法不需要显式求解非线性运动微分方程，就可以得到表征章动的第二欧拉角的解析解。这是用来检查圆锥运动的自由轴对称圆柱受到三个理想化模型的质量损失和新的见解，他们的旋转稳定性。可以看出，角速度的某些配置，这些圆柱体的增长没有限制。尽管有这种现象，所有的配置探讨这里被认为是表现出章动稳定性，在固体火箭发动机的理想属性。
英文摘要：
In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is developed. An analytic solution to the second Euler angle characterising nutation naturally falls out of this method, without explicitly solving the nonlinear differential equations of motion. This is used to examine the coning motion of a free axisymmetric cylinder subject to three idealized models of mass loss and new insight into their rotational stability is presented. It is seen that the angular speeds for some configurations of these cylinders grow without bounds. In spite of this phenomenon, all configurations explored here are seen to exhibit nutational stability, a desirable property in solid rocket motors.
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