Skip to main content

Slow Integral Manifolds

  • 1850 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 2114)

Abstract

In the present chapter we use a method for the qualitative asymptotic analysis of singularly perturbed differential equations by reducing the order of the differential system under consideration. The method relies on the theory of integral manifolds. It essentially replaces the original system by another system on an integral manifold with a lower dimension that is equal to that of the slow subsystem. The emphasis in this chapter is on the study of autonomous systems.

Keywords

  • Autonomous System
  • Invariant Manifold
  • Integral Manifold
  • Invariance Equation
  • Slow Surface

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions
Fig. 2.1
Fig. 2.2
Fig. 2.3
Fig. 2.4
Fig. 2.5
Fig. 2.6
Fig. 2.7
Fig. 2.8
Fig. 2.9
Fig. 2.10

References

  1. Fehrst, A.: Enzyme Structure and Mechanisms. W.F. Freeman, New York (1985)

    Google Scholar 

  2. Kokotović, P.V., Khalil, K.H., O’Reilly, J.: Singular Perturbation Methods in Control: Analysis and Design. SIAM, Philadelphia (1986)

    MATH  Google Scholar 

  3. Pliss, V.A.: A reduction principle in the theory of stability of motion (in Russian, MR 32:7861). Izv. Akad. Nauk SSSR Ser. Mat. 28, 1297–1324 (1964)

    MathSciNet  MATH  Google Scholar 

  4. Sobolev, V.A.: Integral manifolds and decomposition of singularly perturbed systems. Syst. Control Lett. 5, 169–179 (1984)

    CrossRef  MATH  Google Scholar 

  5. Sobolev, V.A., Strygin, V.V.: Permissibility of changing over to precession equations of gyroscopic systems. Mech. Solids 5, 7–13 (1978)

    Google Scholar 

  6. Strygin, V.V., Sobolev, V.A.: Effect of geometric and kinetic parameters and energy dissipation on orientation stability of satellites with double spin. Cosmic Res. 14(3), 331–335 (1976)

    Google Scholar 

  7. Strygin, V.V., Sobolev, V.A.: Asymptotic methods in the problem of stabilization of rotating bodies by using passive dampers. Mech. Solids 5, 19–25 (1977)

    Google Scholar 

  8. Strygin, V.V., Sobolev, V.A.: Separation of Motions by the Integral Manifolds Method (in Russian, MR 89k:34071). Nauka, Moscow (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Shchepakina, E., Sobolev, V., Mortell, M.P. (2014). Slow Integral Manifolds. In: Singular Perturbations. Lecture Notes in Mathematics, vol 2114. Springer, Cham. https://doi.org/10.1007/978-3-319-09570-7_2

Download citation