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Can we solve the functions describing the bend of a cable at rest fixed at two positions?
Assume we have a cable which endpoints is attached to two points at $(x,h)$ and $(x+\Delta_x,h)$.
Further assume it has some mass density distribution, $\rho(m),m \in [0,l]$ and is of some length $l ...
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whats is the applications of the minimization of eigenvalue in the real life ( physics,the natural sciences...)
let $\lambda_{1}(\Omega),\lambda{2}(\Omega),\lambda_{3}(\Omega)...$ the eigenvlues of the laplacian Operator with Dirichlet condition on the boundary on $\Omega $
the classical spectrale optimisation ...
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