Skip to main content
SpringerLink
Log in

Symmetry in discrete mechanics

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

Discrete mechanics, which is motivated by modern digital computer capability, is a form of mechanics in which the basic concepts are defined in terms of differences and sums, while the basic dynamical equations are difference equations. The sophisticated limit concepts of the calculus are thereby replaced by the power to do arithmetic at high speeds. In this paper, it is shown that the physical laws of various forms of discrete mechanics are invariant with respect to the coordinate system used.

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. R. D. Feynman, R. B. Leighton, and M. Sands,The Feynman Lectures on Physics, Vol. I (Addison-Wesley, Reading, Mass., 1963).

    Google Scholar 

  2. D. GreenspanIntroduction to Calculus (Harper and Row, New York, 1968), Chapter II;

    Google Scholar 

  3. Discrete nonlinear string vibrations,The Computer J. 13, 195–201 (1970);

    Google Scholar 

  4. Introduction to Numerical Analysis and Applications (Markham, Chicago, 1971), Chapter VII;

    Google Scholar 

  5. Numerical studies of the three-body problems,SIAM J. Appl. Math. 20, 67–78 (1971);

    Google Scholar 

  6. Numerical approximation of periodic solutions of van der Pol's equation,J. Math. Anal. Appl. 39, 574–579 (1972);

    Google Scholar 

  7. A discrete numerical approach to fluid dynamics, inProc. of IFIPS 71 (North-Holland Publ. Co., Amsterdam, 1972);

    Google Scholar 

  8. New forms of discrete mechanics,Kybernetes 1, 87–101 (1972);

    Google Scholar 

  9. A new explicit discrete mechanics with applications,J. Franklin Inst. 294, 231–240 (1972).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, Madison, Wisconsin

    D. Greenspan

Authors
  1. D. Greenspan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Greenspan, D. Symmetry in discrete mechanics. Found Phys 3, 247–253 (1973). https://doi.org/10.1007/BF00708442

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00708442

Keywords

Search

Navigation