ΛΥΣΕΙΣ ΙΣΟΡΡΟΠΙΑΣ ΚΑΙ ΕΥΣΤΑΘΕΙΑ ΣΕ ΤΡΟΧΙΕΣ ΑΣΤΕΡΟΕΙΔΩΝ ΥΠΟ ΤΗΝ ΕΠΙΔΡΑΣΗ ΑΙΩΝΙΩΝ ΠΑΡΕΛΞΕΩΝ

IN THIS THESIS, WE STUDY THE SECULAR VARIATIONS IN THE RESTRICTED THREE BODY AND, PROPERLY IN THE MODEL SUN-JUPITER- ASTEROID. WE TAKE THE SECULAR PART OF THEDISTURBING FUNCTION UP TO THE FOURTH ORDER WITH RESPECT TO THE ECCENTRICITY AND THE INCLINATION TERMS. WE DEVELOP AN EXPLICIT NUMERICAL METHOD WHICH CONSIST IN A SYSTEMATIC SCANNING OF THE A-H PLANE WHERE A DENOTES THE SEMIMAJOR AXIS AND H STANDS FOR THE DELAUNAY VARIABLE. WE LOCALIZE THE EQUILIBRIUM SOLUTIONS, ASSIGNED TO A PARTICULAR POINT (A-H) OF THE A-H PLANE, AS ROOTS OF A SYSTEM OF TWO NON- LINEAR ALGEBRAIC EQUATIONS. WE THEN DISTINGUISH THE "ACCEPTABLE EQUILIBRIUM SOLUTIONS", (AES). NEXT, WE STUDY THE STABILITY OF THE AES. THE STABILITY ANALYSIS REQUIRED FOR THE HIGHER ORDER TERMS OF OUR EQUATIONS SEEMS TO PRESENT GREAT DIFFICULTIES WHEN VIEWED ACCORDING TO LIAPOUNOV'S METHODOLOGY. THEREFORE, WE DEVELOP AN "EXPLICIT NUMERICAL STABILITY- ANALYSIS TECHNIQUE" WHICH FITS THEFRAMEWORK OF THE PREVIOUS NUMERICAL STRATEGY VERY WELL. WE THEN USE SIXTH-ORDER EXPANSIONS OF THE DISTURBING FUNCTION IN STUDYING BOTH EQUILIBRIUM SOLUTIONS AND STABILITY, BY THE FOREGOING NUMERICAL METHODS. COMPARING THE RESULTS OF THEFOURTH AND THE SIXTH-ORDER THEORIES, WE NOTICE AN INCREASED NUMBER OF THE SIXTH- ORDER AES. ON THE CONTRARY, THE NUMBER OF "STABLE" AES DIMINISHES. IN CONCLUSION, THE SIXTH-ORDER THEORY LEADS TO A DETAILED TOPOGRAPHY OF THE A-H PLANE WITH RESPECT TO THE STABILITY-INSTABILITY" OF THE LOCALIZED AES. SIMILARLY, WE FIND AN UPWARDS EXTREMUM IN THE VALUES OF THE MAXIMUM STABLE INCLINATION (TABLE II) FOR VALUES OF THE SEMI-MAJOR AXIS A BETWEEN 0.40 AND 0.45. APPARENTLY, THIS EXTREMUM EXCEEDS THE VALUE 45 FOR THE INCLINATION I. IN FACT, WHEN TAKING THE SYSTEM SUN-JUPITER-ASTEROID, THIS REGION CORRESPONDS TO THE REGION OF ASTEROIDS WITH LARGE ORBITAL INCLINATIONS. IT SEEMS, THEREFORE, THAT THESE ASTEROIDS WILLBE ON THEIR ORBITS FOR A "LONG-TIME PERIOD".

Grantor dc:publisher

University of Patras

Year dc:date

1990

Author dc:creator

• Φλογαΐτη, Αικατερίνη

• ΑΙΩΝΙΕΣ ΠΑΡΕΛΞΕΙΣ
• Ευστάθεια τροχιών
• ΘΕΣΕΙΣ ΙΣΟΡΡΟΠΙΑΣ
• ΜΕΤΑΒΛΗΤΕΣ DELAUNAY
• ΠΑΡΕΛΚΤΙΚΗ ΣΥΝΑΡΤΗΣΗ
• Περιορισμένο πρόβλημα τριών σωμάτων
• ΤΡΟΧΙΕΣ ΑΣΤΕΡΟΕΙΔΩΝ
• DELAUNAY'S VARIABLES
• DISTURBING FUNCTION
• EQUILIBRIUM SOLUTIONS
• Orbits of asteroids
• Restricted three body problem
• Secular variations
• STABILITY OFORBITS
• Φυσικές Επιστήμες
• Φυσική
• Natural Sciences
• Physical Sciences

Language dc:language

gre

Identifier

10.12681/eadd/1388

OAI identifier oai:identifier

oai:10442/1388