Chebyshev collocation methods for fast orbit determination

We apply some Chebyshev collocation methods for fast and accurate determina tion of ephemeris of artificial satellites. This formulation is based on th e approximation of the differential system by means of Chebyshev polynomial s. In order to assess the convergence of the iterative process and to reduc e the number of operations, the special formulation of Dziobek-Brouwer is u sed. From several numerical tests we conclude that the method presents very good behaviour for geostationary and low eccentric orbits (the most freque nt cases). The number of operations with this method, in some cases, is 20 times less than that with a standard integrator. Besides, a typical dense o utput in a polynomial form is obtained. (C) 1999 Elsevier Science Inc. All rights reserved.