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From the simple Lagrangian the equations of motion for the particle with spinare derived. The spin is shown to be conserved on the particle world-line. Inthe absence of a spin the equation coincides with that of a geodesic. Theequations of motion are valid for massless particles as well, since mass doesnot enter the equations explicitely.Comment: 6 pages, uses mpla1.sty, published in MPLA, replaced with corrected  typo

MOTION OF A VECTOR PARTICLE IN A CURVED SPACETIME I: LAGRANGIAN APPROACH