Conservation laws in three dimensional elasticity

In this thesis all of the conservation laws dependent only on Δu for a system of equations are found. These laws are found from nontrivial solutions of the Euler-Lagrange equations ℒ(u) = 0 of dimensional elasticity. a linearized equation in three The derivation of these equations from a physical situation is first shown. Next, the derivation of the laws linear and then quadratic in Δu is developed followed by the proof that no other laws of higher order exist. The conservation laws found here will generalize previous results from a situation in classical linear elasticity. Lastly, characteristics of the system of equations and their relation to the conservation laws through the calculus of variations and Noether's Theorem are examined.