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
Mass driver then use the mass driver to accelerate pieces of matter of almost any sort, boosting itself in the opposite direction. At the smallest scale of reaction mass, this type of drive is called an ion drive. No absolute theoretical limit is known for the size, acceleration or muzzle energy of linear motors. However, practical engineering constraints apply for such as the power-to-mass ratio, waste heat dissipation, and the energy intake able to be supplied and handled. Exhaust velocity is best neither too low nor too high. There is a mission-dependent limited optimal exhaust velocity and specific impulse for any thruster