Minimum Parametrization of the Cauchy Stress Operator

When D: ξ→η is a linear differential operator, “direct problem” to find the generating compatibility conditions (CC) in form of an operator D1: η→ξ such that Dξ=η implies D1η=0. D involutive, procedure provides successive first order involutive operators D1, ..., Dn, when ground manifold has dimension n, result found by M. Janet as early 1920, footnote. However, link between this “Janet sequence” and “Spencer author paper 1978 still not acknowledged. Conversely, D1 given, more difficult “inverse look for having CC If possible, module defined torsion-free, one shall say parametrized there no relation general D2. The parametrization said be “minimum” if vanishing rank thus torsion module. solution problem, 1995, As applications “differential double duality” theory standard equations physics (Cauchy Maxwell can while Einstein cannot), we do know other references. erator arbitrary dimension=1 control theory, fact controllability “built in” property system, amounting existence depending on choice inputs outputs, even with variable coefficients, acknowledged engineers. Cauchy stress n nevertheless attracted, “separately” without any “guiding line”, many famous scientists (G.B. Airy 1863 = 2, J.C. 1863, G. Morera E. Beltrami 1892 3 , A. 1915 4 ). aim solve minimum problem apply it through effective methods could achieved using computer algebra. Meanwhile, prove all these works are which self-adjoint Ricci showing cannot parametrized, already been exhibited than 20 years before Einstein. byproduct, they based same confusion so-called div induced from Bianchi D2 formal adjoint Killing parametrizing Riemann n. We purely mathematical deeply questions origin gravitational waves. also present similar motivating situation met study contact structures 3. Like Michelson Morley experiment, open historical whether was aware previous or not, but comparison needs comment.