Equations of motion in the gauge gravity models

In the gauge gravitational models, the geometry of a spacetime manifold becomes non-Riemannian. The curvature, torsion and nonmetricity are all nontrivial in these models, in general. The study of the dynamics of the physical matter (particles, bodies, continuous media, etc.) in such manifolds is crucial for determining the actual geometrical structure of the spacetime. Here we briefly describe a model of a test particle with hypermomentum which can be used as a tool for detecting the non-Riemannian geometry, and recall that the conservation laws in the gauge gravity theories underlie the general analysis of the equations of motion in such models.