  We derive the equations of motion in metric-affine gravity by making use of
the conservation laws obtained from Noether's theorem. The results are given in
the form of propagation equations for the multipole decomposition of the matter
sources in metric-affine gravity, i.e., the canonical energy-momentum current
and the hypermomentum current. In particular, the propagation equations allow
for a derivation of the equations of motion of test particles in this
generalized gravity theory, and allow for direct identification of the
couplings between the matter currents and the gauge gravitational field
strengths of the theory, namely, the curvature, the torsion, and the
nonmetricity. We demonstrate that the possible non-Riemannian spacetime
geometry can only be detected with the help of the test bodies that are formed
of matter with microstructure. Ordinary gravitating matter, i.e., matter
without microscopic internal degrees of freedom, can probe only the Riemannian
spacetime geometry. Thereby, we generalize previous results of general
relativity and Poincare gauge theory.
