A fourth order nonlinear two point boundary value problem arising in linear elasticity

摘要

The shape of a length of wire confined to the surface of a sphere with its ends tangent to two given circles of lattitude and otherwise free, in its most relaxed state, is found by solving a variational problem to be the solution of a fourth order nonlinear two point boundary value problem. A scheme of numerical computation is outlined which avoids a nearby singularity.