Advertisement

Moscow University Mechanics Bulletin

, Volume 74, Issue 5, pp 118–122 | Cite as

Motion of a Puck on a Rotating Horizontal Plane

  • A. V. KarapetyanEmail author
Article
  • 1 Downloads

Abstract

The motion of a puck on a horizontal plane rotating about a vertical axis with dry friction is considered. It is assumed that the Coulomb law of dry friction is locally valid at each point belonging to the lower surface of the puck. The resultant force and friction torque are determined according to the dynamically consistent model of contact stresses. This problem generalizes the problem of motion of a puck on a fixed plane and the motion of a disk (a puck of zero height) on a rotating plane. The invariant sets of the problem are found and their properties are studied. In the case of a sufficiently small Coulomb friction coefficient, the general solution to the equations of motion of the puck is constructed as a power series expansion with respect to this coefficient.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00338).

References

  1. 1.
    A. P. Popov, “Dynamically Consistent Model of Contact Stresses for Planar Motion of a Rigid Body,” Prikl. Mat. Mekh. 73 (2), 199–203 (2007) [J. Appl. Math. Mech. 73 (2), 134–144 (2007)].Google Scholar
  2. 2.
    T. V. Sal’nikova, D. V. Treshchev, and S. R. Gallyamov, “Motion of a Free Hollow Disk on a Rough Horizontal Plane,” Nelin. Din. 8 (1), 83–101.Google Scholar
  3. 3.
    A. V. Karapetyan, “The Movement of a Disc on a Rotating Horizontal Plane with Dry Friction,” Prikl. Mat. Mekh. 80 (5), 535–540 (2016) [J. Appl. Math. Mech. 80 (5), 376–380 (2016)].MathSciNetGoogle Scholar
  4. 4.
    A. I. Grudev, A. Yu. Ishlinskii, and F. L. Chernous’ko, “On the Motion of a Particle over a Rough Rotating Plane,” Prikl. Mat. Mekh. 53 (3), 372–381 (1989) [J. Appl. Math. Mech. 53 (3), 281–288 (1989)].MathSciNetzbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

Personalised recommendations