Skip to main content
SpringerLink
Log in

Symbolic-numerical methods of studying equilibrium positions of a gyrostat satellite

  • Computer Algebra
  • Published:
Programming and Computer Software Aims and scope Submit manuscript

Abstract

Methods of computer algebra are used to study properties of a nonlinear algebraic system that determines equilibrium positions of a gyrostat satellite moving along a circular orbit. Bifurcation values of parameters such that the number of equilibrium positions changes are found numerically. Detailed numerical analyses of evolution of existence domains of different numbers of equilibria in the space of dimensionless parameters are performed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sarychev, V.A., Problems of orientation of satellites, in Itogi Nauki Tekh., Ser.: Issled. Kosm. Prostr., vol. 11, Moscow: VINITI, 1978.

    Google Scholar 

  2. Sarychev, V.A. and Mirer, S.A., Relative equilibria of a gyrostat satellite with internal angular momentum along a principal axis, Acta Astronautica, 2001, no. 49, pp. 641–644.

    Google Scholar 

  3. Sarychev, V.A., Mirer, S.A., and Degtyarev, A.A., The dynamics of a satellite-gyrostat with a single nonzero component of the vector of gyrostatic moment, Cosmic Res., 2005, vol. 43, no. 4, pp. 268–279.

    Article  Google Scholar 

  4. Sarychev, V.A., Mirer, S.A., and Degtyarev, A.A., Dynamics of a gyrostat satellite with the vector of gyrostatic moment in the principal plane of inertia, Cosmic Res., 2008, vol. 46, no. 1, pp. 60–73.

    Article  Google Scholar 

  5. Longman, R.W., Gravity-gradient stabilization of gyrostat satellites with rotor axes in principal planes, Celestial Mech., 1971, vol. 3, pp. 169–188.

    Article  MATH  MathSciNet  Google Scholar 

  6. Longman, R.W., Hagedorn, P., and Beck, A., Stabilization due to gyroscopic coupling in dual-spin satellites subject to gravitational torques, Celestial Mech., 1981, vol. 25, pp. 353–373.

    Article  MATH  MathSciNet  Google Scholar 

  7. Sarychev, V.A. and Gutnik, S.A., Relative equilibria of a gyrostat satellite, Cosmic. Res., 1984, vol. 22, no. 3, pp. 257–260.

    Google Scholar 

  8. Gutnik, S.A., Symbolic-numeric investigation of the aerodynamic forces influence on satellite dynamics, Computer Algebra in Scientific Computing, 2011, vol. 6885, pp. 192–199; Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V., Eds., CASC 2011, LNCS.

    Article  Google Scholar 

  9. Buchberger, B., Theoretical basis for the reduction of polynomials to canonical forms, SIGSAM Bull., 1976, vol. 10, no. 3, pp. 19–29.

    Article  MathSciNet  Google Scholar 

  10. Char, B.W., Geddes, K.O., Gonnet, G.H., Monagan, M.B., and Watt, S.M., Maple Reference Manual, Waterloo, Canada: Watcom, 1992.

    Google Scholar 

  11. http://www.wolfram.com/mathematica

  12. Sarychev, V.A., Gutnik, S.A., Silva A., and Santos L., Dynamics of gyrostat satellite subject to gravitational torque. Investigation of equilibria, Preprint of Keldysh Inst. of Appl. Math., Russ. Acad. Sci., Moscow, no. 63, 2012; http://www.keldysh.ru/papers/2012

    Google Scholar 

  13. Gutnik, S.A. and Sarychev, V.A.: Symbolic-numerical investigation of gyrostat satellite dynamics, Computer Algebra in Scientific Computing, 2013, vol. 8136, pp. 169–178; Gerdt, V.P., Koepf, W., Mayr, E.W., and Vorozhtsov, E.V., Eds., CASC 2013, LNCS.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700, Russia

    S. A. Gutnik & V. A. Sarychev

  2. Moscow Institute of International Relations, pr. Vernadskogo 76, Moscow, 119454, Russia

    S. A. Gutnik & V. A. Sarychev

  3. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    S. A. Gutnik & V. A. Sarychev

Authors
  1. S. A. Gutnik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Sarychev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Gutnik.

Additional information

Original Russian Text © S.A. Gutnik, V.A. Sarychev, 2014, published in Programmirovanie, 2014, Vol. 40, No. 3.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gutnik, S.A., Sarychev, V.A. Symbolic-numerical methods of studying equilibrium positions of a gyrostat satellite. Program Comput Soft 40, 143–150 (2014). https://doi.org/10.1134/S0361768814030049

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0361768814030049

Keywords

Search

Navigation