Deviation equations in spaces with affine connection
  Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained on this base. This is done via imposing certain conditions on the Lie derivatives with respect to the tangential vector of the basic trajectory. 
Bozhidar Z. Iliev and Sawa S. Manoff (Institute for Nuclear Research   and Nuclear Energy, Bulgarian Academy of Sciences, So...