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28 March 2024
 
  » arxiv » math-ph/0611051

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A Generalized Montgomery Phase Formula for Rotating Self Deforming Bodies
Alejandro Cabrera ;
Date 21 Nov 2006
Subject Mathematical Physics
AbstractWe 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 $Delta T$, this curve is simple and closed, the deforming body ’{}s orientation in space is fully characterized by an angle or phase $ heta_{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.
Source arXiv, math-ph/0611051
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