Advertisement

Mechanics of Solids

, Volume 51, Issue 2, pp 148–155 | Cite as

Equations and algorithms for determining the inertial attitude and apparent velocity of a moving object in quaternion and biquaternion 4D orthogonal operators

  • Yu. N. Chelnokov
Article

Abstract

We consider equations and algorithms describing the operation of strapdown inertial navigation systems (SINS) intended for determining the inertial attitude parameters (the Rodrigues–Hamilton (Euler) parameters) and the apparent velocity of a moving object. The construction of these equations and algorithms is based on the Kotelnikov–Study transference principle, Hamiltonian quaternions and Clifford biquaternions, and differential equations in four-dimensional (quaternion and biquaternion) orthogonal operators.

Keywords

moving object real and dual Rodrigues–Hamilton (Euler) parameters inertial attitude apparent velocity Kotelnikov–Study transference principle Hamiltonian quaternions Clifford biquaternions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. N. Chelnokov, Quaternion and BiquaternionModels andMethods ofMechanics of Solids and Their Applications. Geometry and Kinematics of Motion (Fizmatlit, Moscow, 2006) [in Russian].Google Scholar
  2. 2.
    Yu. N. Chelnokov, L. A. Chelnokova, and S. E. Perelyaev, “New Equations and Algorithms of SINS Operation Based on the Kotelnikov–Study Superposition and Transference Principles,” in Proc. 17th Intern. Conf. “System Analysis, Control, and Navigation” (Izdat. MAI,Moscow, 2012), pp. 49–51 [in Russian].Google Scholar
  3. 3.
    Yu. N. Chelnokov, “Kotelnikov–Study Superposition and Transference Principles in Inertial Navigation and Motion Control,” in Proc. 18th Intern. Conf. “System Analysis, Control, and Navigation” (Izdat. MAI, Moscow, 2013), pp. 124–126 [in Russian].Google Scholar
  4. 4.
    Yu. N. Chelnokov and S. E. Perelyaev, “New Equations and Algorithms of SINS Operation Constructed Using the Kotelnikov–Study Superposition and Transference Principles,” in in Proc. XXth St. Petersburg Intern. Conf. on Integrated Navigation Systems (State Scientific Center of the Russian Federation, OOO “Concern ‘TsNII Elektropribor’,” St. Petersburg, 2013), pp. 54–57 [in Russian].Google Scholar
  5. 5.
    Yu. N. Chelnokov, “One Form of the Inertial Navigation Equations,” Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 20–28 (1981) [Mech. Solids (Engl. Transl.)].ADSGoogle Scholar
  6. 6.
    Yu. N. Chelnokov, “On Integration of Kinematic Equations of a Rigid Body’s Screw-Motion,” Prikl. Mat. Mekh. 44 (1), 32–39 (1980) [J. Appl.Math. Mech. (Engl. Transl.) 44 (1), 19–23 (1980)].MathSciNetMATHGoogle Scholar
  7. 7.
    Yu. N. Chelnokov, “On Stability of Solutions to Biquaternion Kinematic Equations of Helical Motion of Solids,” in Collection of Sci.-Method. Papers on Theor.Mech., No. 13 (Vysshaya Shkola,Moscow, 1983), pp. 103–109 [in Russian].Google Scholar
  8. 8.
    Yu. N. Chelnokov, “Inertial Navigation Equations for the Apparent and Gravitational Velocities and Their Analytic Solutions for an ImmovableObject,” Izv. Akad.Nauk.Mekh. Tverd. Tela, No. 1, 6–18 (2016) [Mech. Solids (Engl. Transl.) 51 (1), 1–11 (2016)].Google Scholar
  9. 9.
    V. N. Branets and I. P. Shmyglevskii, Introduction to the Theory of Strapdown Inertial Navigation Systems (Nauka, Moscow, 1992) [in Russian].MATHGoogle Scholar
  10. 10.
    A. P. Kotelnikov, Helical Calculus and Some of Its Applications to Geometry and Mechanics (Kazan, 1895) [in Russian].Google Scholar
  11. 11.
    A. P. Kotelnikov, “Screws and ComplexNumbers,” Izv. Fiz.-Mat.Obshch. Imper. Kazan. Univ. Ser. 2, No. 6, 23–33 (1896).Google Scholar
  12. 12.
    A. P. Kotelnikov, “Theory of Vectors and Complex Numbers,” in Several Applications of Lobachevskii’s Ideas in Mechanics and Physics, Collection of Papers (Gostekhizdat, Moscow, 1950), pp. 7–47 [in Russian].Google Scholar
  13. 13.
    F.M. Dimentberg, Theory of Screws and Its Applications (Nauka, Moscow, 1978) [in Russian].Google Scholar
  14. 14.
    A. Edvards, “Strapdown Inertial Navigation Systems,” Vopr. Raketn. Tekhn., No. 5, 50–57 (1973).Google Scholar
  15. 15.
    P. N. Besarab, “Determination of the Spatial Attitude Parameters of a Moving Object,” Zh. Vychisl. Mat. Mat. Fiz. 14 (1), 240–246 (1974) [USSR Comput. Math. Math. Phys. (Engl. Transl.) 14 (1), 242–248 (1974)].MathSciNetGoogle Scholar
  16. 16.
    V. N. Branets, Lectures on the Theory of Strapdown Inertial Navigation Systems (MFTI,Moscow, 2009) [in Russian].Google Scholar
  17. 17.
    A. P. Panov, Mathematical Foundations of the Theory of Inertial Attitude (Naukova Dumka, Kiev, 1995) [in Russian].Google Scholar

Copyright information

© Allerton Press, Inc. 2016

Authors and Affiliations

  1. 1.Institute for Precision Mechanics and Control ProblemsRussian Academy of SciencesSaratovRussia
  2. 2.Chernyshevskii Saratov State UniversitySaratovRussia

Personalised recommendations