| Summary: | <p>The work objective is the synthesis of simple analytical formula of the optimal roll angle of hypersonic gliding vehicles for conditions of quasi-horizontal motion, allowing its practical implementation in onboard control algorithms.<br />The introduction justifies relevance, formulates basic control tasks, and describes a history of scientific research and achievements in the field concerned. The author reveals a common disadvantage of the other authors’ methods, i.e. the problem of practical implementation in onboard control algorithms.<br />The similar tasks of hypersonic maneuvers are systemized according to the type of maneuver, control parameters and limitations.<br />In the statement of the problem the glider launched horizontally with a suborbital speed glides passive in the static Atmosphere on a spherical surface of constant radius in the Central field of gravitation.<br />The work specifies a system of equations of motion in the inertial spherical coordinate system, sets the limits on the roll angle and optimization criteria at the end of the flight: high speed or azimuth and the minimum distances to the specified geocentric points.<br />The solution.<br />1) A system of equations of motion is transformed by replacing the time argument with another independent argument – the normal equilibrium overload. The Hamiltonian and the equations of mated parameters are obtained using the Pontryagin’s maximum principle. The number of equations of motion and mated vector is reduced.<br />2) The mated parameters were expressed by formulas using current movement parameters. The formulas are proved through differentiation and substitution in the equations of motion.<br />3) The Formula of optimal roll-position control by condition of maximum is obtained. After substitution of mated parameters, the insertion of constants, and trigonometric transformations the Formula of the optimal roll angle is obtained as functions of the current parameters of motion.<br />The roll angle is expressed as the ratio of the sine of the latitude by the cosine of the suborbital inclination with correction for the speed.<br />The spherical diagram shows the geometric illustration of the trajectory and control parameters. <br />In conclusion the paper shows the essence and the solution novelty, describes the flight model, which allowed us to conduct numerical tests of the Formula. Besides, it concludes that the formula is valid and can be used in practical implementation in on-Board algorithms to control the hypersonic gliding vehicles.</p>
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