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 density unit of mass, formula_9, is equal to the product of its linear mass density, formula_10, and the infinitesimal unit of length, formula_11: The linear mass density can then be understood as the derivative of the mass function with respect to the one dimension of the rod (the position along its length formula_13) The SI unit of linear mass density is the kilogram per meter (kg/m). Linear density of fibers and yarns can be measured by many methods. The simplest one is to measure a length of material and weigh it. However, this requires a large sample and masks the variability