TL;DRAbstract
The free rotation in space of flexible polygonal structures about their axes is studied. The large deformation equations are formulated, resulting in a set of sixth order nonlinear differential equations. The governing parameter B represents the relative importance of centrifugal forces to flexural rigidity. Perturbation solutions are obtained for small B. The equations are also integrated numerically by quasi-Newton and homotopy methods. Forces, moments, and maximum deformations are determined for polygons of three to six sides and B up to 100. At very large B, the polygons deform into a circle.
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The free rotation in space of flexible polygonal structures about their axes is studied. The large deformation equations are formulated, resulting in a set of sixth order nonlinear differential equations. The governing parameter B represents the relative importance of centrifugal forces to flexural rigidity. Perturbation solutions are obtained for small B. The equations are also integrated numerically by quasi-Newton and homotopy methods. Forces, moments, and maximum deformations are determined for polygons of three to six sides and B up to 100. At very large B, the polygons deform into a circle.
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