Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T08:44:19.053Z Has data issue: false hasContentIssue false
  • English
  • Français

Ignorable coordinates and steady motion in classical mechanics

Published online by Cambridge University Press:  24 October 2008

C. W. Kilmister  and
F. A. E. Pirani
C. W. Kilmister
Affiliation:
King's College, London and Brandeis University, Waltham, Massachusetts
F. A. E. Pirani
Affiliation:
King's College, London and Brandeis University, Waltham, Massachusetts
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown, for a classical dynamical system with a Lagrangian, that the existence of an ignorable coordinate is equivalent to the vanishing of a certain Lie derivative. On this covariant description is based a new definition of steady motion. A definition given earlier by Synge is criticized.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 211 - 222
Copyright
Copyright © Cambridge Philosophical Society 1965

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Eisenhart, L. P.Continuous groups of transformations (Princeton, 1933).Google Scholar
(2)Kilmister, C. W.Edinburgh Math. Notes No. 44 (1961), 13–16.Google Scholar
(3)Routh, E. J.Dynamics of a system of rigid bodies (London, 1905).Google Scholar
(4)Schoutten, J. A.Ricci-Calculus (Berlin, 1954).CrossRefGoogle Scholar
(5)Synge, J. L.Philos. Trans. Roy. Soc. London, Ser. A 226 (1926), 31–106.Google Scholar
(6)Whittaker, E. T.Analytical dynamics (Cambridge, 1927).Google Scholar
(7)Yano, K.The theory of the Lie derivative and its applications (North Holland; Amsterdam, 1955).Google Scholar