UBC Theses and Dissertations
The stability of body centered polygonal vortex line configurations Mertz, Gordon J.
This thesis is concerned with the stability of rectilinear vortex line configurations. A method for consideration of stability problems, using the equations of motion for small perturbations about equilibrium, is developed; and the free energy criterion for stability stated. The former method is used in analyzing the stability of the body centered polygonal configuration, which is a Thomson polygon centered by a vortex of arbitrary relative circulation; the latter criterion is applied to the Thomson heptagon stability question. The main results are that a Thomson polygon of any order can be stabilized by a large enough central circulation and that the Thomson heptagon is stable.
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