ΥΠΑΡΞΗ ΛΥΣΕΩΝ ΤΟΥ ΑΝΤΙΣΤΡΟΦΟΥ ΠΡΟΒΛΗΜΑΤΟΣ ΤΗΣ ΔΥΝΑΜΙΚΗΣ ΣΤΟΝ ΤΡΙΣΔΙΑΣΤΑΤΟ ΧΩΡΟ

THIS WORK DEALS WITH THE FUNDAMENTAL QUESTION OF THE POSSIBILITY OF THE DETERMINATION OF THE POTENTIAL FIELD FROM TWO PARAMETRIC FAMILIES OF ORBITS OF A MASS POINT MOVING IN THIS FIELD. THE PRESENT THESIS IS CLOSELY RELATED TO THE WORK BY VARADI AND ERDI (1983). IN FACT THE CONCLUSION REGARDING THE EXISTANCE OF A SOLUTION IS DIFFERENT FROM THEIRS AND THIS IS DUE TO THE FACT THAT WE FORMULATE THE PROBLEM IN A DIFFERENT WAY. THE ESSENTIAL DIFFERENCE BETWEEN THE TWO STUDIES REFERS NOT ONLY TO THE METHOD BUT ALSO TO THE FINAL CONCLUSION. VARADI AND ERDI CONCLUDE THAT, IN GENERAL, THE PROBLEM ADMITS OF A SOLUTION IF THE FAMILY OFCURVES AND THE ENERGY ARE GIVEN. ON THE CONTRARY, WE CONCLUDE THAT, FOR A GIVEN TWO PARAMETRIC FAMILY OF SPACE CURVES F(X,Y,Z)=C1 G(X,Y,Z)=C2, IN GENERAL, NOPOTENTIAL U=U(X,Y,Z) EXISTS WHICH CAN GIVE RISE TO THIS FAMILY. HOWEVER, IF THE GIVEN FUNCTIONS F(X,Y,Z) AND G(X,Y,Z) SATISFY CERTAIN CONDITIONS, THE CORRESPONDING POTENTIAL U(X,Y,Z) AS WELL AS THE TOTAL ENERGY E=E(F,G) CAN BE DETERMINED UNIQUALLY, APART FROM A MULTIPLICATIVE AND AN ADDITIVE CONSTANT. IT CAN BE SAID THAT THIS WORK CONSTITUTES A COMPLETE SOLUTION OF THE THREE DIMENSIONAL INVERSE PROBLEM AS IT IS SEEN FROM THE THEORY DEVELOPED IN CHAPTER 1 AND FROM THE EXAMPLES PRESENTED IN CHAPTER 2.

Grantor dc:publisher

Aristotle University Of Thessaloniki (AUTH)

Year dc:date

1987

Author dc:creator

• Nakhla, Atef

• FAMILY OF CURVES
• Inverse problem
• SELESTIAL MECHANICS
• THREE DIMENSION
• TWO PARAMETRIC FAMILY
• Αντίστροφο πρόβλημα
• ΔΙΠΑΡΑΜΕΤΡΙΚΗ ΟΙΚΟΓΕΝΕΙΑ
• ΟΙΚΟΓΕΝΕΙΑ ΚΑΜΠΥΛΩΝ
• ΤΡΙΣΔΙΑΣΤΑΤΟ
• Φυσικές Επιστήμες
• Φυσική
• Natural Sciences
• Physical Sciences

Language dc:language

gre

Identifier

10.12681/eadd/0449

OAI identifier oai:identifier

oai:10442/0449