Active Rocket Trajectory Arcs: A Review

Abstract

This paper reviews the development of analytical, approximate analytical, and numerical methods for solving the variational problem on the determination of optimal rocket trajectories in gravitational fields, and their application to study flight dynamics. Specifics of these methods as applied to solve modern and complex problems are described. A variational problem is formulated and extremal thrust arcs are described. Papers containing results of analytical investigations on thrust arcs are reviewed in depth. Partially investigated problems are described. Problems of great interest in the development of methods for solving the variational problem and problems in the theory of optimal trajectories are mentioned.

Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems

“…The purpose of this paper is to investigate optimal control problems governed by systems of ordinary differential equations of the forṁ Many models that enter into this framework can be found in practice and, in particular, in the existing literature. Among these we can mention: the Goddard's problem in three dimensions [24] analyzed in Bonnans et al [11], several models concerning the motion of rockets as the ones treated in Lawden [33], Bell and Jacobson [8], Goh [26,29], Oberle [40], Azimov [7] and Hull [31]; an hydrothermal electricity production problem studied in Bortolossi et al [13], the problem of atmospheric flight considered by Oberle in [41], and the optimal production processes studied in Cho et al [16] and Maurer at al. [36].…”