Derivation of the equation of caustics in cartesian coordinates with maple

Ioakimidis, NI; Anastasselou, EG

dc.contributor.author	Ioakimidis, NI	en
dc.contributor.author	Anastasselou, EG	en
dc.date.accessioned	2014-03-01T01:09:50Z
dc.date.available	2014-03-01T01:09:50Z
dc.date.issued	1994	en
dc.identifier.issn	0013-7944	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11198
dc.subject.classification	Mechanics	en
dc.subject.other	Algebra	en
dc.subject.other	Algorithms	en
dc.subject.other	Computer software	en
dc.subject.other	Computer systems	en
dc.subject.other	Cracks	en
dc.subject.other	Elasticity	en
dc.subject.other	Cartesian coordinates	en
dc.subject.other	Cartesian equation	en
dc.subject.other	Equation of caustics	en
dc.subject.other	Equivalent unique equation	en
dc.subject.other	Grobner bases algorithm	en
dc.subject.other	Maple V computer system	en
dc.subject.other	Parametric equation	en
dc.subject.other	Software package - GROBNER	en
dc.subject.other	Fracture mechanics	en
dc.title	Derivation of the equation of caustics in cartesian coordinates with maple	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/0013-7944(94)90151-1	en
heal.identifier.secondary	http://dx.doi.org/10.1016/0013-7944(94)90151-1	en
heal.language	English	en
heal.publicationDate	1994	en
heal.abstract	The well-known equation of caustics about crack tips in experimental fracture mechanics is usually expressed in the form of two equations for the Cartesian coordinates (x,y) with a parameter (an appropriate polar angle playing the rǒle of this parameter). Here we derive the equivalent unique equation (but without a parameter) also in Cartesian coordinates with the help of the computer algebra system Maple V by using the available Gröbner-bases algorithm. The obtained Cartesian equation is of the sixth degree and it can be solved in closed form with respect to y yielding an explicit result y =y(x). The same equation is also checked in two special cases, where it gives the same results as the equivalent pair of parametric equations. Analogous, more general results can also be derived. © 1994.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Engineering Fracture Mechanics	en
dc.identifier.doi	10.1016/0013-7944(94)90151-1	en
dc.identifier.isi	ISI:A1994NK57600015	en
dc.identifier.volume	48	en
dc.identifier.issue	1	en
dc.identifier.spage	147	en
dc.identifier.epage	149	en