Abstract
AbstractThe differential equation describing the drag of a Cottrell atmosphere by a dislocation appears in a number of other physical moving‐frame‐of‐reference problems related to line sources of vector fields, such as vortices in fluid flow and line sources of heat. It reduces to the so‐called modified Mathieu equation. This equation is solved and the asymptotic behavior of the modified Mathieu functions is determined in the limiting situations of small velocity and small or large distance from the line source. A specific asymptotic form of the function of the second kind is found to behave like a K‐Bessel function in the limit of the argument z approaching ∞ and like an I‐Bessel function in the limit z → ∞. The solution can be used to obtained analytical results for the Cottrellatmosphere problem.
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