Corresponding author: Molodenkov A. V., Ph. D., Senior Researcher, Laboratory of Mechanics, Navigation and Motion Control, Precision Mechanics and Control Problems Institute, RAS, Saratov, 410028, Russian Federation,
e-mail: iptmuran@san.ru

Received on July 05, 2016
Accepted on July 1, 2016

The problem of the optimal turn in the sense of minimum of energy loss of a spacecraft as a rigid body with one axis of symmetry is considered in the quaternion statement. For simplifying problem (concerning dynamic Euler equations), we change the variables reducing the original optimal turn problem of axially symmetric spacecraft to the problem of optimal turn of the rigid body with spherical mass distribution including one new scalar equation. Using the Pontryagin maximum principle, a new analytical solution of this problem in the class of conical motions is obtained. Algorithm of the optimal turn of a spacecraft is given. An explicit expression for the constant in magnitude optimal angular velocity vector of a spacecraft is found. The motion trajectory of a spacecraft is regular precession. The conditions for the initial and terminal values of a spacecraft angular velocity vector are formulated, which make it possible to solve the problem analytically in the class of conical motions. The initial and the terminal vectors of spacecraft angular velocity must be on the conical surface generated by arbitrary given constant conditions of the problem. The numerical example is presented. The example contain reorientation of the Space Shuttle in the class of conical motions.
Keywords: optimal control, spacecraft, axially symmetric rigid body, conical motion

For citation:

Sapunkov Ya. G., Molodenkov A. V. Algorithm of the Optimal in the Sense of Minimum of Energy Loss Turn of an Axially Symmetric Spacecraft in the Class of Conical Motions, Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 1, pp. 134—143.
DOI: 10.17587/mau.18.134-143

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