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Kinematically, the elastic deflection in a solid can be traced back to 3 irreducible types of deformation {Dil, Rot, Dev}: The dilatation Dil is defined by the div-operator, the change in direction Rot by the rot-operator and the shape change Dev by the dev-operator. These deformations are automatically determined thanks to the mathematical well known identities rot grad = 0 and div rot = 0 and are subject to the longitudinal, transverse and deviatoric wave equations. All 3 types of waves are based on a local Euler momentum balance and can be confirmed physically by the impedance theorem and mathematically by factorization. The longitudinal and transverse waves are space waves that are free of transverse expansion in a medium that is unlimited on all sides. The deviation wave is divergence- and rotation-free and describes a surface wave. All 3 types of equations are partial differential equations (PDG 1st order) and provide for the homogeneous solid the same solutions as the classic Cauchy wave equation (=PDG 2nd order) and simplify the calculation of inhomogeneous waveguides.
