Please see the attached document for a summary of my proof of rigidity.
The question implies that the author defines the two terms "rigid" and "elastic" as somehow incompatible? Than, due to SUCH definition and since the term
"vibrating" is a feature due to the presence of elasticity - is not it? - one needs to acknowledge that a "vibrating string" is obligatory elastic?
Are you saying the rigid string cannot vibrate? What about Gauss's theorema egregium? It says a surface can bend without the distance between two points increasing.
Here is the Hamiltonian equation for loops on the string:
Of course, things that bend always elongate if they have the Pythagorean metric. But we are taking about the string in the Lagrangian configuration or Hamiltonian phase space which is a 2-dimenional subspace of euclidean space formed by the potential energy surface of the string.
Oh, by the way anyone know how to introduce potential energy to the elastic string? Its impossible according to V.I Arnold Mathematical Methods in Classical Mechanics. Checkout what he says about the theory of oscillation with one degree of freedom.
It simply cannot be true the string does not conserve energy! You cannot prove it does not. But that is your challenge if you want to defend physics and mathematics on the string theory. Prove the string is not symplectic!
And if the string can only vibrate in one mode, what are you going to do with strings in higher dimension? If higher dimensional strings are not isomorphic on the natural string in Euclidean space, then don't you guys need to get another name for your theory? :)
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