Study of optimized spacecraft motion under conditions of limitation of heat transfer

Spacecraft heating during reentry is studied for trajectory optimization during atmospheric entry, of spacecraft behavior over each point from initial to terminal velocity, for heat transfer when the carrier-resistance ratio is maximal for horizontal flight, and for state variables expressing maximum heat transfer and minimum oscillation. Equations of motion and drag coefficient for entry at small angles are given and optimal conditions are defined for Mayer variations for continuous curves with minimums at specific intervals satisfying the Euler-Lagrange equations. A transcendental equation is developed which is useful for analyzing total flight behavior. Stability is formulated as a spherical region whose state space is bounded, and a solution of equations of motion, though not bounded by the region, tends to converge asymptotically at the center of sphere origin.