Classical Mechanics of Spinning Patricle in a Curved Space

An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian formalism for this system and possible method for its quantization are discussed. It is shown that the Hamilton equations coincide with the Papapetrou equations for spinning test-particle in general relativity.