Abstract: A new formulation is presented in this paper,where the following vari ables are taken as a set of generalized coordinates:the radial distance,the latitude and the right ascension of the centre of mass(CM)of the tethered system as well as the tether length and two Euler angles,in the meridian plane and out of the meridian plane,of the tether line relative to the radial vector from the centre of the Earth to the CM.The equations of motion are derived by using the Lagrangian formulas,where the tether is modelled as an elastic continuum with mass but remains straight.The Earth's gravitational potential perturbation and atmospheric drag are taken into account.All classic orbital elements and usual angular motion parameters can be calculated with the new set of generalized coordinates and their rates.