NON-HAMILTONIAN UNNORMALIZED QUATERNIONS OF HALF-ROTATION IN ALGORITHMS OF STRAPDOWN INERTIAL SYSTEMS

A. P. Panov, S. A. Ponomarenko

Abstract


The application of non-Hamiltonian unnormalized quaternions of half-rotation in algorithmsof strapdown inertial systems is considered in the article. Non-Hamiltonian unnormalized quaternionscan be zero in contrast to the classical Hamiltonian normalized quaternion with the parameters of theEuler (Rodrigues–Hamilton), their rates are not constant and depend on the Euler angles of final rotation

Keywords


Unnormalized quaternions of rotation; half-rotation; groups and algebras of quaternions; strapdown inertial systems; guidance; navigation; control

References


V. N. Branets and I. P. Shmyglevskiy, Introduction to the theory of strapdown inertial navigation systems Moscow: Nauka, 1992. 278 p.

M. V. Sinkov, J. E. Boyarinova and J. A. Kalinowski, The finite dimension hypercomplex number systems. Fundamentals of the theory. Applications. Kyiv: Institute for information recording NAS of Ukraine. 2010. 389 p.

V. F. Zhuravlev, Foundations of theoretical mechanics. Moscow: Phismathlit, 2008. 304 p.

S. N. Kirpichnikov and V. S. Novoselov, Mathematical aspects of the kinematics of a rigid body. Leningrad: Publishing House of Leningrad University, 1986. 250 p.

A. P. Panov, V. V. Tsysarzh and V. V. Aksenov, “On the new quaternion methods for solving problems of orientation, navigation and control for the strapdown inertial systems”. VII St. Petersburg International Conference on Integrated Navigation Systems. Proc. rep. St. Petersburg. 2000, May 29-31, pp. 115–117.

A. P. Panov, “On the application of unnormalized quaternion rotations of five-dimensional vectors and their algebra in the inertial orientation”. VIII International scientific-technical Conference “Girotehnologii, navigation and traffic control”, Kyiv, “KPI”, 21-22 April 2011. Collection of papers. Part I, pp. 131–137. URL: http://pskla.kpi.ua/index.php/materiali-konferentsij.

A. P. Panov, “Methods of sixth-order accuracy for calculations of the orientation vector coordinates by the quasicoordinates”. Cybernetics and Computer Science, ALLERTON PRESS, New York, 1986. vol. 69, pp. 47–52.

A. P. Panov, “Optimization algorithms of highly accurate calculations of quaternions in the case of the precession of a rigid body”. Cybernetics and Computer Science, ALLERTON PRESS, New York, 1987. vol. 73, pp. 3–9.

A. P. Panov, Mathematical foundations of the theory of inertial orientation. Kyiv, Naukova dumka, 1995. 279 p.

A. P. Panov, “On new unnormalized quaternions of solid body rotation”. Problems of Analytical Mechanics and its Applications. Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Vol. 26, 1999, pp. 300–329.

A. G. Kurosh, Lectures on General Algebra. Moscow. Phismathlit, 1973. 399 p.

I. L. Kantor and A. S. Solodovnikov, Hypercomplex numbers. Moscow: Nauka, 1973. 143 p.

V. A. Demenkov, Y. A. Kuznetsov and A. P. Panov, “Using reference models of rotation for estimation of orientation algorithms in unnormalized quaternions of strapdown navigation systems”. 17th International Conference on Automatic Control “Automatics–2010”. Collection of papers. vol. 2. Kharkiv, National University of Radio Electronics, 2010, pp. 45–47.

V. Z. Gusinsky, V. M. Lesyuchevsky, Y. A. Litmanovich, Musoff Howard and Schmidt T. George. “A New Procedure for Optimized Strapdown Attitude Algorithms”. Journal of Guidance, Control and Dynamics. 1997. vol. 20. no. 4, pp. 673–680.

J. Mark and D. Tazartes. “Tapered algorithms that take into account non-ideality of the frequency response of the output signals of gyroscopes”. Gyroscopy and navigation. 2000. no. 1 (28), pp. 65–77.

S. E. Perelyaev, G. I. Chesnokov and A. V. Chernodarov, “Experience in development and design problems of autonomous precision SINS aerospace”. IV International scientific-technical Conference “Girotehnologii, navigation, traffic management and the construction of aerospace engineering”. Kyiv: “KPI”, 26-

April 2007. Collection of reports, pp. 29–37.

Y. A. Litmanovich and J. Mark, “Progress in the development of algorithms for SINS in the West and the East with the materials of the St. Petersburg conference: review of a decade”. X St. Petersburg International Conference on Integrated Navigation Systems. Proc. rep. St. Petersburg. 2003, May 26-28, pp. 250–260.

A. P. Panov, “Adaptive algorithms for calculations precession quaternion rotation of a rigid body”. Cybernetics and Computer Science, ALLERTON PRESS, New York, 1988. vol. 77, pp. 47–52.

S. P. Kryukov, G. I. Chesnokov and V.A. Troitskiy, “Experience in the development and certification of strapdown inertial navigation system for civil aviation (SINS-85) and creation on its basis of modifications to control the movement of sea, land and aerospace objects and tasks of geodesy and gravimetry”. IX St. Petersburg International Conference on Integrated Navigation Systems. Proc. rep. St. Petersburg. 2002, May 27-29, pp. 190–197.

G. I. Chesnokov and A. M. Golubev, “Strapdown inertial navigation systems for modern aviation”. X St. Petersburg International Conference on Integrated Navigation Systems. Proc. rep. St. Petersburg. 2003, May 26-28, 192 p.

A. G. Kuznetsov, B. I. Portnov and E. A. Izmailov, “Development and testing of two classes of aircraft strapdown inertial navigation systems on the laser gyro”. Gyroscopy and navigation. 2014. no. 2 (85), pp. 3–12.

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