Representation theory of the Galilean group to , and applying Hamilton's equations, we obtain the mass-velocity relation . The hypersurface is parametrized by this velocity In . Consider the stabilizer of a point on the orbit, (), where the velocity is . Because of transitivity, we know the unitary irrep contains a nontrivial linear subspace with these energy-momentum eigenvalues. (This subspace only exists in a rigged Hilbert space, because the momentum spectrum is continuous.) The subspace is spanned by , , and . We already know how the subspace of the irrep transforms under all operators but the angular momentum. Note that the rotation subgroup is
Linear elasticity fourth-order stiffness tensor, formula_8 is the body force per unit volume, formula_9 is the mass density, formula_10 represents the nabla operator, formula_11 represents a transpose, formula_12 represents the second derivative with respect to time, and formula_13 is the inner product of two second-order tensors (summation over repeated indices is implied). Expressed in terms of components with respect to a rectangular Cartesian coordinate system, the governing equations of linear elasticity are: An elastostatic boundary value problem for an isotropic-homogeneous media is a system of 15 independent equations and equal number of unknowns (3 equilibrium equations, 6 strain-displacement equations, and 6 constitutive