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.
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