SpringerLink
Log in

Some theorems for determining the definiteness and changeability of sign of functions and the application to the conditional stability of the motion of the axis of a slee** top

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

This paper gives some theorems for determining the definiteness and changeability of sign of functions as well as the application to the axis of a slee** top. The necessary and sufficient condition of the conditional stability of the motion is obtained, which coincides with that of the stability of nutation angle and also with that of the stability of total variables in the equations of motion.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Maievsky, N.V., on the effect of spinning motion on the flight of oblong shells in air, spb., (1865).

  2. Routh, E.J., The advanced part of a treatise on the dynamics of a system of rigid bodies. Dover Publications. (1955).

  3. Joukowsky, N.E., On the Solidity of Motions, (1882), Complete Works, Vol. 1, OGIZ, (1948), 67–160.

    Google Scholar 

  4. Klein, F., On the stability of a slee** top, Bulletin of the American Mathematical Society, ser. 2, Vol. III, (1897, 129–132, 292.

    Google Scholar 

  5. Grammel, R., Die Stabilitat der Standeschen Kreiselbewegungen, Mathematische Zeitschrift, Bd 6, (1920), 124–142.

    Google Scholar 

  6. Synge, J.L., Griffith, B.A., Principles of Mechanics, second edition, (1949), 440.

  7. Synge, J.L., Classical Mechanics, Handbuch der Physik, Band III/I, (1960), 90.

    Google Scholar 

  8. Chetayev, N.G., On the stability of spinning motion of a shell, PMM, 10, 1, (1946), 135–138.

    Google Scholar 

  9. Chetayev, N.G., On the stability of the rotation of a rigid body with a fixed point in Lagrange's case, PMM, 18, 1 (1954), 123–124.

    Google Scholar 

  10. Ge Zheng-ming, On the necessary and sufficient condition of the unconditional stability of the motion of Lagrange's vertical top, Journal of Shanghai Chiaotung University, No. 1, (1979), 53–59. (in Chinese).

    Google Scholar 

  11. Loicjansky, L.G., Lourie, A.E., A Text of Theoretical Mechanics, Vol. II, (1955), 572–573.

    Google Scholar 

  12. Rumjancev, V.V., On the stability of the permanent rotation of a rigid body about a fixed point, PMM, 19, 3, (1957), 339–346.

    Google Scholar 

  13. Magnus, K., On the stability of the motion of heavy symmetric gyroscope in Cartan suspension, PMM, 22, 2, (1958), 173–178.

    Google Scholar 

  14. Malkin, I.G., Theory of Stability of Motions, Nauka, Moscow, (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Teaching and Research Section of General Mechanics, Department of Engineering Mechanics, Shanghai Jiao-tong University, Shanghai, China

    Ge Zheng-ming

Authors
  1. Ge Zheng-ming
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng-ming, G. Some theorems for determining the definiteness and changeability of sign of functions and the application to the conditional stability of the motion of the axis of a slee** top. Appl Math Mech 2, 757–764 (1981). https://doi.org/10.1007/BF01897646

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01897646

Keywords

Search

Navigation