Skip to main content
SpringerLink
Log in

The Transgression Effect in the Problem of Motion of an Almost Holonomic Pendulum

  • MECHANICS
  • Published:
Vestnik St. Petersburg University, Mathematics Aims and scope Submit manuscript

Abstract

In 1986, Ya.V. Tatarinov presented the basis of the theory of weakly nonholonomic systems. Mechanical systems with nonholonomic constraints depending on a small parameter are considered. It is assumed that when the value of this parameter is zero, the constraints of such a system become integrable; i.e., in this case, we have a family of holonomic systems depending on several arbitrary integration constants. We will assume that these holonomic systems are completely integrable Hamiltonian systems. When the small parameter is not zero, the behavior of such systems can be considered with the help of asymptotic methods representing their motion as a combination of the motion of a slightly modified holonomic system with slowly varying previous integration constants (the transgression effect). In this paper, we describe the transgression effect in the problem of motion of an almost holonomic pendulum.

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

REFERENCES

  1. Ya. V. Tatarinov, “Weakly nonholonomic systems,” in Proc. 6th All-Union Conf. on Theoretical and Applied Mechanics, Tashkent, Sept. 24–30, 1986 (FAN, Tashkent, 1986).

  2. Ya. V. Tatarinov, “Weakly nonholonomic representation of the problem of the rolling of a solid and the possibility of averaging over phase tori,” Mekh. Solids 23, 538–545 (1988).

    Google Scholar 

  3. Ya. V. Tatarinov, Nonholonomic Systems in Comparison with Hamiltonian Ones, Doctoral Dissertation in Mathematics and Physics (Moscow, 1990).

  4. Ya. V. Tatarinov, “Consequences of non-integrable perturbation of integrable constraints: Non-linear effects of motion near the equilibrium manifold,” J. Appl. Math. Mech. 56, 507–517 (1992).

    Article  MathSciNet  Google Scholar 

Download references

Funding

The work was supported by the Russian Foundation for Basic Research, grants nos. 19-01-00140 and 20-01-00637.

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, 119234, Moscow, Russia

    A. S. Kuleshov & I. I. Ulyatovskaya

Authors
  1. A. S. Kuleshov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. I. Ulyatovskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. S. Kuleshov or I. I. Ulyatovskaya.

Ethics declarations

The authors declare that they have no conflict of interest.

Additional information

Translated by E. Smirnova

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kuleshov, A.S., Ulyatovskaya, I.I. The Transgression Effect in the Problem of Motion of an Almost Holonomic Pendulum. Vestnik St.Petersb. Univ.Math. 56, 594–597 (2023). https://doi.org/10.1134/S1063454123040209

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063454123040209

Keywords:

Search

Navigation