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Derivation of the equation of caustics in cartesian coordinates with maple
This item is provided by the institution :
National Technical University of Athens
Repository :
Digital Library of National Technical University of Athens | Dspace@NTUA
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ΕΚΤ item type
Journal part
(EN)
Scientific article
(EN)
EKT year
1994
(EN)
EKT historical period
Title
Derivation of the equation of caustics in cartesian coordinates with maple (EN)
Creator
Anastasselou, EG (EN)
Ioakimidis, NI (EN)
Description
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)
Type
journalArticle (EN)
Subject
Grobner bases algorithm (EN)
Fracture mechanics (EN)
Computer software (EN)
Equivalent unique equation (EN)
Elasticity (EN)
Software package - GROBNER (EN)
Equation of caustics (EN)
Cartesian equation (EN)
Cracks (EN)
Computer systems (EN)
Algebra (EN)
Algorithms (EN)
Mechanics (EN)
Maple V computer system (EN)
Cartesian coordinates (EN)
Parametric equation (EN)
Provider
National Technical University of Athens
Repository / collection
Digital Library of National Technical University of Athens | Dspace@NTUA
Subcollections
Κεντρική Βιβλιοθήκη Ε.Μ.Π.
Ιδρυματικό Αποθετήριο
Δημοσιεύσεις μελών Δ.Ε.Π. σε περιοδικά
Journal
Engineering Fracture Mechanics (EN)
Language
English
Issued
1994 (EN)
Identifier
http://hdl.handle.net/123456789/11198
10.1016/0013-7944(94)90151-1 (EN)
1 (EN)
0013-7944 (EN)
48 (EN)
147 (EN)
149 (EN)
ISI:A1994NK57600015 (EN)
Publisher
PERGAMON-ELSEVIER SCIENCE LTD (EN)
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