Skip to main content
SpringerLink
Log in

Cycloidal pendulum with a rolling cylinder

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

Free vibrations of a heavy homogeneous cylinder rolling in a cylindrical cavity whose directing curve is a brachistochrone are considered. The equation of motion of the cylinder is derived and the circular frequency of free vibrations of the cylinder center of mass is determined. An analogy between the cycloidal pendulum with a rolling cylinder and the classical cycloidal pendulum in the form of a material point is obtained.

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. V. P. Legeza, Vibroprotection of Dynamical Systems by Roller Dampers (Chetverta Khvilya, Kiev, 2010) [in Ukrainian].

    Google Scholar 

  2. V. P. Legeza, “Quickest-Descent Curve in the Problem of Rolling of a Homogeneous Cylinder,” Prikl. Mekh. 44(12), 131–138 (2008) [Int. Appl.Mech. (Engl. Transl.) 44 (12), 1430–1436 (2008)].

    MathSciNet  MATH  Google Scholar 

  3. V. P. Legeza, “Brachistochrone for a Rolling Cylinder,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 34–41 (2010) [Mech. Solids (Engl. Transl.) 45 (1), 27–33 (2010)].

  4. L. D. Akulenko, “An Analog of the Classical Brachistochrone for a Disk,” Dokl. Ross. Akad. Nauk 419(2), 193–196 (2008) [Dokl. Phys. (Engl. Transl.) 53 (3), 156–159 (2008)].

    MathSciNet  Google Scholar 

  5. L. D. Akulenko, “The Brachistochrone Problem for a Disc,” Prikl. Mat. Mekh. 73(4), 520–530 (2009) [J. Appl. Math.Mech. (Engl. Transl.) 73 (4), 371–378 (2009)].

    MathSciNet  Google Scholar 

  6. E. Rogers, “Brachistochrone and Tautochrone Curves for Rolling Body,” Am. J. Phys. 14(4), 249–242 (1964).

    Article  ADS  Google Scholar 

  7. K. Magnus, Vibrations. Introduction to the Study of Oscillatory Systems (Mir, Moscow, 1982) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National University of Food Technologies, Vladimirskaya 68, Kiev, 01601, Ukraine

    V. P. Legeza

Authors
  1. V. P. Legeza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. P. Legeza.

Additional information

Original Russian Text © V.P. Legeza, 2012, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2012, No. 4, pp. 11–15.

About this article

Cite this article

Legeza, V.P. Cycloidal pendulum with a rolling cylinder. Mech. Solids 47, 380–384 (2012). https://doi.org/10.3103/S0025654412040024

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654412040024

Keywords

Search

Navigation