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A Generalized Montgomery Phase Formula for Rotating Self Deforming Bodies

Alejandro Cabrera
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Abstract

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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BibTeXRIS

Alejandro Cabrera. 2006-11-20. A Generalized Montgomery Phase Formula for Rotating Self Deforming Bodies. https://doi.org/10.1016/j.geomphys.2006.11.003

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