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We present a simple method to derive the semiclassical equations of motionfor a spinning particle in a gravitational field. We investigate the cases ofclassical, rotating particles (pole-dipole particles), as well as particleswith intrinsic spin. We show that, starting with a simple Lagrangian, one canderive equations for the spin evolution and momentum propagation in theframework of metric theories of gravity and in theories based on aRiemann-Cartan geometry (Poincare gauge theory), without explicitly referringto matter current densities (spin and energy-momentum). Our results agree withthose derived from the multipole expansion of the current densities by theconventional Papapetrou method and from the WKB analysis for elementaryparticles.Comment: 28 page

Mathisson–Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation