Astronomy and Astrophysics – Astrophysics
Scientific paper
May 1953
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1953rspsa.217..327j&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 217, Issue 1130, pp. 327-343
Astronomy and Astrophysics
Astrophysics
1
Scientific paper
The purpose of this paper is to present a new method of approach to certain problems in mechanics which give rise to ordinary non-linear differential equations of the second order. The method, which is based on the topology of the integral curves of a first-order differential equation, aims at providing qualitative information which can be used, if necessary, in guiding numerical calculations of the solutions. Among the equations discussed are those of Emden and Blasius, which occur in astrophysics and in boundary-layer theory respectively; these, together with the equation of a basic problem of internal ballistics, are shown to be reducible to different forms of the same first-order equation, which is itself of a type studied originally by Poincare in another connexion.
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