Analytical calculations of a spacecraft motion path in atmosphere

Аuthors

Sokolov N. L.

Central Research Institute of Machine Building, 4, Pionerskaya st., Korolev, Moscow region, 141070, Russia

Abstract

Employing analytical methods for computing spacecraft movement trajectories seems effective while solving a number of problems of practical importance. Analysis of the existing methods reveals that they are based mainly on mathematical models of spacecraft flight along a fore-and-aft plane, as well as some simplified spacecraft motion in space equations. It limits the possibility of their use while solving a number of space exploration problems of practical importance. The paper describes an analytical method for spacecraft atmosphere movement parameters computation. The scientific novelty of the developed method consists in transformation of a number functions in the form of recurrent piecewise-constant dependencies at the finite intervals of spacecraft flight trajectories.

After transformation of initial system of differential equations, we obtained the final computation dependencies for velocity and flight altitude, trajectory and course angles, longitudinal and cross range via the atmospheric density. Selection of such an argument, namely atmospheric density results from the fact that spacecraft flight situations can be identified based on calculations of this parameter with further recommendations for control decision-making. Based on the obtained equations we can compute not only the coordinates of spacecraft atmosphere movement, but evaluate the main characteristics, effecting design and technological decision making while a spacecraft design. Particularly, the fast evaluation of maximum overloads values, affecting a spacecraft in aerodynamic deceleration phases is provided. Analytic dependencies can be used while solving a number of variational problems in the conditions of preliminary definition of spacecraft control structure.

The tabular matter and graphical data are presented. Computation errors of spacecraft motion trajectory parameters are analyzed. It is shown that these computation errors do not exceed 2-3% with the total qualitative matching of obtained data and of differential equations numerical integration results. Employing of the developed analytical method allows obtain the highly precise computation results of spacecraft motion parameters in the atmosphere. The developed formulas provide high speed of calculations for a wide range of initial data, boundary conditions, and can form the base for spacecraft onboard control algorithms development.

Keywords:

spacecraft motion equations, descent vehicle trajectory calculation analytical method, aerodynamic flight stage coordinates computation recursion relations, analytical method computational errors

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