English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

First integrals of this system resulting from conservation of linear momentum, angular momentum, and energy are well known. Moreover, the use of these integrals has led to a number of explicit reductions of (1.1) from order eighteen to order six. (A complete bibliography of the earlier methods of reduction can be found in [1, Chapter 2]; more recent methods are those of Whittaker [2, pp. 339-351], Wintner [3, pp. 306-319], and Wintner and van Kampen [4].) The fact that the first integrals of linear and angular momentum are due to the invariance of a Newtonian system under the Galilean group is also well known; this invariance has been used in one form or another in most of the more recent reductions, usually in the form of contact transformations. In this paper, it will be shown that the entire reduction of (1.1) is the result of its invariance under continuous transformation groups, and also that the use of these groups will, for practical purposes, give no further reduction of the system. In order to demonstrate the equivalence of the reductions, the necessary coordinate changes will be patterned on those given by Whittaker; similar results could be obtained by following any of the classical methods. We will begin with a brief review of the theory of continuous transformation

A reduction of the three body problem by means of transformation groups