Basic Theorems in Dynamic Elasticity - UNAM

Reciprocity Theorem(Betti’s Theorem)If displacement field u due to a body force f, boundary conditions on S andinitial conditions at t 0 induce traction T(u,n), and displacement field v due toa body force g, boundary conditions on S and initial conditions at t 0 inducetraction T(v,n), thus the following scalar equality holds:Homework:Prove Betti’s TheoremEnrico Betti (1823-1892) was an Italian“mathematician who wrote a pioneering memoiron topology, the study of surfaces and higherdimensionalspaces, and wrote one of the firstrigorous expositions of the theory of equationsdeveloped by the noted French mathematicianEvariste Galois” (Encyclopaedia Britannica)