Phugoid oscillations in optimal reentry trajectories

A major problem with operations of lifting reentry vehicle having an aft center-of-gravity location due to large engine mass at the rear is the required hypersonic trim to fight the desired trajectory. This condition is most severe for lifting maneuvers. As a first step toward analyzing this problem, this paper considers the lift requirement for some basic maneuvers in the plane of a great circle. Considerations are given to optimal lift control for achieving the maximization of either the final altitude, speed or range. For the maximum-range problem, phugoid oscillation along an optimal trajectory is less severe as compared to a glide with maximum lift-to-drag ratio. An explicit formula for the number of oscillations for an entry from orbital speed is proposed.     

Optimal aeroassisted return from high earth orbit with plane change

This paper gives a complete analysis of the problem of aeroassisted return from a high Earth orbit to a low Earth orbit with plane change. A discussion of pure propulsive maneuver leads to the necessary change for improvement of the fuel consumption by inserting in the middle of the trajectory an atmospheric phase to obtain all or part of the required plane change. The variational problem is reduced to a parametric optimization problem by using the known results in optimal impulsive transfer and solving the atmospheric turning problem for storage and use in the optimization process. The coupling effect between space maneuver and atmospheric maneuver is discussed. Depending on the values of the plane change i, the ratios of the radii, $\text{n =}\text{r}{}_1\text{r}{}_2$ between the orbits and $\text{a =}\text{r}{}_2\text{R}$ between the low orbit and the atmosphere, and the maximum lift-to-drag ratio E1 of the vehicle, the optimal maneuver can be pure propulsive or aeroassisted. For aeroassisted maneuver, the optimal mode can be parabolic, which requires only drag capability of the vehicle, or elliptic. In the elliptic mode, it can be by one-impulse for deorbit and one or two-impulse in postatmospheric flight, or by two-impulse for deorbit with only one impulse for final circularization. It is shown that whenever an impulse is applied, a plane change is made. The necessary conditions for the optimal split of the plane changes are derived and mechanized in a program routine for obtaining the solution.     

Deceleration and heating constrained footprint of shuttle vehicles

With increasing frequency in shuttle operation, it is of interest to have more than one or two landing fields within the boundary of the reachable area of the reentry vehicle. This boundary, called the footprint, depends on the aerodynamic characteristics of the vehicle and is severely restricted by the deceleration and heating constraints imposed upon the atmospheric reentry trajectory. This paper gives a general assessment of the footprint as a function of various deceleration and heating constraints. The difficulties in the computation of the three-dimensional reentry trajectories with optimal modulation in both the angle-of-attack and the bank angle are alleviated by the following devices: (a) nondimensionalizing of the equations of motion and use of the density as the altitude variable; (b) use of the classical integrals of the motion; (c) transformation of the adjoint variables into physical variables; and (d) spherical rotation of the coordinates.     

The darboux point and the conjugate point on optimal deorbit for reentry trajectories

The concept of the Darboux point at which an extremal loses its global optimality is extended to the case of discontinuous control. Using Contensou's domain of maneuverability, the condition for optimal switching at a corner is derived and the optimality of the trajectory in the neighborhood of a Darboux point is analyzed. The theory is applied to the problems of minimum-fuel planar and noncoplanar deorbit from elliptical orbits for atmospheric entry at a prescribed angle. In each case, the global optimal trajectory is assessed and it is found that in these nonlinear problems the Darboux point and the conjugate point are distinct. The global optimality is always lost before local optimality.