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Derivation of the equation of caustics in cartesian coordinates with maple

โœ Scribed by Nikolaos I. Ioakimidis; Eleni G. Anastasselou

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
242 KB
Volume
48
Category
Article
ISSN
0013-7944

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โœฆ Synopsis

Alastract-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 role 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 Griibner-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.

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