Regularization of certain systems of differential equations
dc.contributor.author | Benson, Dean | |
dc.contributor.department | Mathematics | |
dc.date | 2018-08-23T08:27:00.000 | |
dc.date.accessioned | 2020-06-30T07:24:33Z | |
dc.date.available | 2020-06-30T07:24:33Z | |
dc.date.copyright | Fri Jan 01 00:00:00 UTC 1954 | |
dc.date.issued | 1954 | |
dc.description.abstract | <p>Certain types of systems of differential equations of the form d2x dt2-2l x,ydy dt=Wx , d2ydt2 +2lx,y dxdt=W y, 5.1 have been regularized in this paper. The regularizations by both Levi-Civita and Birkhoff for the equations of motion in the restricted problem of three bodies were discussed;Hill's equations arising in a problem of celestial mechanics were of the form of equations (5.1). This system of equations has one singular point and was regularized by a transformation similar to that used by Levi-Civita. The equations of motion for the restricted problem of n-bodies, for n ≧ 4, were regularized for three of their singular points by using transformations of the type employed by Birkhoff two times in succession. For n = 4 the system was completely regularized, since there were only three singular points;In section IV the system of equations d2x dt2-2l x,ydy dt=-nxr n+2, d2ydt2 +2lx,y dxdt=- nyrn+2 , 5.2 with the integral dxdt 2+d ydt 2=2rn- C 5.2' was considered. It was determined that transformations of the type z = wk would regularize equations (5.2) for values of n in the interval -2 < n < 2 when the proper choice of k was made. It was shown that one should choose k = 2 when -2 < n < 0, and k ≧ 42-n for 0 < n < 2. While this selection for values of k regularizes equations (5.2) for all values of n in the interval -2 < n < 2, there is a better choice for k if n is in the interval 1 ≦ n < 2. When n lies in this last interval, choose k by equation (4.4) which gives k = 22-n . Examples using these transformations in removing singularities in systems of differential equations of the type (5.2) have been given.</p> | |
dc.format.mimetype | application/pdf | |
dc.identifier | archive/lib.dr.iastate.edu/rtd/12890/ | |
dc.identifier.articleid | 13889 | |
dc.identifier.contextkey | 6866446 | |
dc.identifier.doi | https://doi.org/10.31274/rtd-180813-14154 | |
dc.identifier.s3bucket | isulib-bepress-aws-west | |
dc.identifier.submissionpath | rtd/12890 | |
dc.identifier.uri | https://dr.lib.iastate.edu/handle/20.500.12876/66308 | |
dc.language.iso | en | |
dc.source.bitstream | archive/lib.dr.iastate.edu/rtd/12890/r_DP11952.pdf|||Fri Jan 14 19:32:20 UTC 2022 | |
dc.subject.disciplines | Mathematics | |
dc.subject.keywords | Differential equations | |
dc.title | Regularization of certain systems of differential equations | |
dc.type | article | |
dc.type.genre | dissertation | |
dspace.entity.type | Publication | |
relation.isOrgUnitOfPublication | 82295b2b-0f85-4929-9659-075c93e82c48 | |
thesis.degree.level | dissertation | |
thesis.degree.name | Doctor of Philosophy |
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