Skip to main content
SpringerLink
Log in

Gradient systems and mechanical systems

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

All types of gradient systems and their properties are discussed. Two problems connected with gradient systems and mechanical systems are studied. One is the direct problem of transforming a mechanical system into a gradient system, and the other is the inverse problem, which is transforming a gradient system into a mechanical system.

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. Hirsch, M.W., Smale, S.: Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, New York (1974)

  2. McLachlan, R.I., Quispel, G.R.W., Robidoux, N.: Geometric integration using discrete gradients. Philos. Trans. R. Soc. Lond. A 357, 1021–1045 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Mei, F.X.: On gradient systems. Mech. Eng. 34, 89–90 (2012) (in Chinese)

  4. Mei, F.X., Wu, H.B.: A gradient representation for generalized Birkhoff system. J. Dyn. Control 10, 289–292 (2012) (in Chinese)

  5. Mei, F.X., Cui, J.C., Wu, H.B.: A gradient representation and a fractional gradient representation of Birkhoff system. Trans. Beijing Inst. Technol. 32, 1298–1300 (2012) (in Chinese)

  6. Lou, Z.M., Mei, F.X.: A second order gradient representation of mechanics system. Acta Phys. Sin. 61, 024502 (2012) (in Chinese)

  7. Mei, F.X., Wu, H.B.: Generalized Hamilton system and gradient system. Sci. Sin.-Phys. Mech. Astron. 43, 538–540 (2013) (in Chinese)

  8. Chen, X.W., Zhao, G.L., Mei, F.X.: A fractional gradient representation of the Poincaré equations. Nonlinear Dyn. 73, 579–582 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Mei, F.X.: On skew-gradient systems. Mech. Eng. 35, 79–81 (2013) (in Chinese)

  10. Mei, F.X.: Analytical Mechanics (II). Beijing Institute of Technology Press, Beijing (2013) (in Chinese)

  11. Mei, F.X., Wu, H.B.: A gradient representation of first-order Lagrange system. Acta Phys. Sin. 62, 214501 (2013) (in Chinese)

  12. Mei, F.X., Wu, H.B.: Generalized Birkhoff system and a kind of combined gradient system. Acta Phys. Sin. 64, 184501 (2015) (in Chinese)

  13. Wu, H.B., Mei, F.X.: A gradient representation of holonomic system in the event space. Acta Phys. Sin. 64, 234501 (2015) (in Chinese)

  14. Mei, F.X., Wu, H.B.: Skew-gradient representation of generalized Birkhoffian system. Chin. Phys. B 24, 104502 (2015)

    Article  Google Scholar 

  15. Mei, F.X., Wu, H.B.: Two kinds of generalized gradient representations for holonomic mechanical systems. Chin. Phys. B 25, 014502 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The project was supported by the National Natural Science Foundation of China (Grant 11272050).

Author information

Authors and Affiliations

  1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Fengxiang Mei

  2. School of Mathematics, Beijing Institute of Technology, Beijing, 100081, China

    Huibin Wu

Authors
  1. Fengxiang Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huibin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huibin Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mei, F., Wu, H. Gradient systems and mechanical systems. Acta Mech. Sin. 32, 935–940 (2016). https://doi.org/10.1007/s10409-016-0580-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-016-0580-4

Keywords

Search

Navigation