旋转自形变体的广义Montgomery相位公式
A Generalized Montgomery Phase Formula for Rotating Self Deforming Bodies
摘要：
本文研究了角动量不为零的自形变体的运动，当形状变化是时间的函数时。相对于质心的守恒角动量，当从旋转坐标系看时，描述了一条球体上的曲线，就像刚体运动一样，尽管服从一个更复杂的非自治方程。我们观察到，如果在时间$ΔT$之后，这条曲线是简单的和封闭的，则变形体在空间中的取向完全由角度或相位$θ_{M}$表征。我们还给出了这个角的重建公式，推广了R。Montgomery著名的刚体相公式。最后，我们应用这些技巧，在一些具体的例子中得到的变形体的运动的分析结果。
英文摘要：
We study the motion of self deforming bodies with non zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame, describes a curve on a sphere as it happens for the rigid body motion, though obeying a more complicated non-autonomous equation. We observe that if, after time $ΔT$, this curve is simple and closed, the deforming body \'{}s orientation in space is fully characterized by an angle or phase $θ_{M}$. We also give a reconstruction formula for this angle which generalizes R. Montgomery\'{}s well known formula for the rigid body phase. Finally, we apply these techniques to obtain analytical results on the motion of deforming bodies in some concrete examples.
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