Skip to main content
SpringerLink
Log in

Hydrostatics in weak force fields. On annular figures of equilibrium of a rotating liquid and their stability

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

We consider the problem of annular equilibrium figures of a rotating weightless liquid, having surface tension, and their stability. This question has been studied by Charreaux (for a discussion of his results see [1]), who examined the evolution of the forms of annular equilibrium figures and showed that there exists a family of stable equilibrium shapes. However, these studies of Charreaux are incomplete, and the conclusion on the existence of stable forms is valid only for axisymmetric disturbances.

In the following we examine the properties of annular equilibrium figures of a rotating liquid. From the results of numerical integration on a digital computer we construct a family of equilibrium forms and present data which permit finding the corresponding equilibrium form from the ensemble of physical parameters which define the equilibrium state. In studying the stability we use the technique of [2, 3].

The results of the numerical calculation and the asymptotic representat ons show that stable annular equilibrium figures of a rotating liquid do not exist.

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. P. Appell, Equilibrium Figures for a Rotating Homogeneous Liquid [Russian translation], ONTI, 301–312, 1936.

  2. A. D. Tyuptsov, “Hydrostatics in weak force fields. Stability of equilibrium forms of a liquid surface”, Izv. AN SSSR, MZhG [Fluid Dynamics], no. 2, 1966.

  3. M. A. Belyaeva, L. A. Slobozhanin, and A. D. Tyuptsov, “Hydrostatics in weak force fields”, collection: Mathematical Methods in Space Vehicle Dynamics, no. 6. Introduction to Dynamics of a Body with a Liquid under Conditions of Weightlessness [in Russian], Izd. VTs AN SSSR, 1968.

  4. L. A. Slobozhanin, “Hydrostatics in weak force fields. Equiliforms of the surface of a rotating liquid under conditions of weightlessness”, Izv. AN SSSR, MZhG [Fluid Dynamics], no. 5, 1966.

  5. V. V. Rumyantsev, “On the stability of motion of a rigid body with a liquid having surface tension”, PMM, vol. 28, no. 4, 1964.

  6. N. N. Moiseev and V. V. Rumyantsev, Dynamics of a Body with Cavities Containing a Liquid [in Russian], Nauka, Moscow, 168–186, 1965.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Khar'kov

    L. A. Slobozhanin

Authors
  1. L. A. Slobozhanin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author wishes to thank M. A. Belyaev for compiling the program for the numerical calculation, and also N. D. Kopachevskii, A. D. Myshkis, and A. D. Tyuptsov for discussions of the results and helpful remarks.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Slobozhanin, L.A. Hydrostatics in weak force fields. On annular figures of equilibrium of a rotating liquid and their stability. Fluid Dyn 3, 41–45 (1968). https://doi.org/10.1007/BF01019190

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01019190

Keywords

Search

Navigation