The parameter optimization method is used to solve the optimal trajectory for vertical ascent to the GEO with dynamic pressure and thrust acceleration constraints. The time derivative of the velocity magnitude of the vehicle is assumed to be a polynomial function of the flight time, with the coefficients as free parameters to be selected.
The required thrust magnitude and angle are derived as functions of the state variables and the polynomial. A first order polynomial function is adopted for numerical computation. The flight time and the two coefficients are selected such that the final condition for GEO insertion is satisfied and the final mass is maximized. With thrust acceleration constraints, it is found that the final mass remaining is 0.1165, 3.414, 10.53, 18.48, and 25.90 percent, respectively. For a
vertically ascending trajectory, the relative speed of the vehicle with respect to the atmosphere is the vertical component of the inertial vehicle velocity.
關聯:
43rd Congress of the International Astronautical Federation,
