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Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 12, pp. 847—855
DOI: 10.17587/mau.18.847855
Quasioptimal Algorithm of Turn of an Axially Symmetric Spacecraft under Arbitrary Boundary Conditions
Ya. G. Sapunkov, iptmuran@san.ru, A. V. Molodenkov, iptmuran@san.ru Precision Mechanics and Control Problems Institute of RAS, Saratov, 410028, Russian Federation

Corresponding author:
Molodenkov Aleksei V., Ph. D., Senior Researcher, Laboratory of Mechanics, Navigation and Motion Control, Precision Mechanics and Control Problems Institute, RAS, Saratov, 41))28, Russian Federation, email: iptmuran@san.ru
Accepted on August 31, 2017
The traditional problem of optimal turn in the sense of minimum of energy loss of an axally symmetric spacecraft as a rigid body under arbitrary boundary conditions on angular position and angular velocity of a spacecraft without constraint on the function of control is considered in the quaternion statement. The spacecraft reorientation time is arbitrary and fixed. Using substitutions of variables, the original problem is simplified (in terms of dynamic Euler equations) to the optimal slew problem for a rigid body with a spherical mass distribution. The simplified problem contains one additional scalar differential equation. In the class of generalized conical motions, the traditional optimal slew problem is modified to obtain analytical solutions for motion equations. The solutions contain arbitrary constants and two arbitrary scalar functions (generalized conical motion parameters). An optimization problem is formulated and solved with respect to these two functions, the second derivatives of which serve as controls in the optimization problem. The resulting analytical solution of the modified problem can be treated as an approximate (quasioptimal) solution of the traditional optimal slew problem under arbitrary boundary conditions. The quasioptimal algorithm of the optimal turn of a spacecraft is given. Numerical examples showing the closeness of the solutions of the traditional and modified optimal slew problems for an axially symmetric spacecraft are given.
Keywords: axially symmetric rigid body, spacecraft, optimal turn, quasioptimal solution, generalized conical motion, arbitrary boundary conditions

For citation:
Sapunkov Ya. G., Molodenkov A. V. Quasioptimal Algorithm of Turn of an Axially Symmetric Spacecraft under Arbitrary Boundary Conditions, Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18,
no. 12, pp. 847—855.
DOI: 10.17587/mau.18.847855
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