Gfodesic structure

The relative dynamics of test bodies moving along geodesics in a torsion-free affine space is considered. The treatment is based on systematic use of the exponential mapping. An exact equation of the relative motion is obtained, to which the equation of geodesic deviation is the first approximation. An algorithm is constructed for deriving the equations for successive approximations. For the case of a Riemannian connection, the Lagrangian and Hamiltonian formalisms are considered and the basic integrals of the motion are studied. Applications in the general theory of relativity are discussed.