Abstract:
In accordance with the Kirchhoff analogy, the equilibrium equations of the
elastic thread on a plane are equivalent to the equations of motion of a simple
pendulum. This analogy is generalized to the case when the thread lays on a smooth
curved surface. We derive the equilibrium equations of the threads in the general
case and in the particular cases of planar, cylindrical and spherical surfaces.
For these surfaces the Kirchhoff analogy is generalized to the case of a simple
pendulum in an additional force field. There are also considered the electromagnetic
and nonholonomic analogies for the equilibrium equations of an elastic thread.
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