No abstract

The Hamiltonian formulation of the constant radial propulsive acceleration problem in nondimensional units reveals that the problem does not depend on any physical parameter. The qualitative description of the integrable flow is given in terms of the energy and the angular momentum, showing that the different regimes are the result of a bifurcation phenomenon. The solution via the Hamilton-Jacobi equation demonstrates that the elliptic integrals of the three kinds are intrinsic to the problem.

No abstract

In the context of general perturbation theories, we analyze the motion of an artificial satellite around an Earth-like planet perturbed by the first eight zonal harmonic coefficients. By means of two Lie transforms and the Krylov-Bogoliubov-Mitropolsky method we produce a closed-form second-order analytical theory. Except for the critical inclination, this theory is valid for small eccentricities and inclinations. Two orbit propagators are derived from the analytical theory. The first, PPKBZ9~, is completely analytical whereas the second, PPKBZ99'~, is based on numerical methods that compute the transformation of the variables. Prediction accuracy given by the orbit propagator programs is investigated by using data of different types of Earth and Mars orbiters. PPKBZ9~ can also be used by means of a friendly Web Interface in S'lstrody¥:ils Web Site.

A higher-order perturbation theory for the rotation of a uniaxial satellite under gravity-gradient torque demonstrates that known special configurations of the attitude dynamics at which the satellite rotates, on average, as in a torque-free state, are only the result of an early truncation of the secular frequencies of motion. In addition to providing a deeper insight into the dynamics, the higher order of the analytical solution makes it competitive when compared with the long-term numerical integration of the equations of motion.