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Most experimental laboratories accelerate and rotate relative to inertial frames. This paper derives approximate expressions for the general-relativistic metric and the general-relativistic equations of motion of freely falling particles in such a laboratory. The metric is derived accurate to second order in distance from the origin of coordinates; the equations of motion are derived accurate to first order. The equations of motion contain inertial, Coriolis, and centripetal pseudoforces, electric, magnetic, and magnetic-magnetic type forces due to Riemann curvature (inhomogeneous gravity), "gravitational red-shift" corrections to these forces, and velocity-induced special-relativistic corrections.
Ni et al. (Wed,) studied this question.