ΠΕΡΙΟΔΙΚΕΣ ΚΑΙ ΑΣΥΜΠΤΩΤΙΚΕΣ ΛΥΣΕΙΣ ΓΥΡΩ ΑΠΟ ΑΣΤΑΘΗ ΣΗΜΕΙΑ ΙΣΟΡΡΟΠΙΑΣ ΣΤΟ ΠΡΟΒΛΗΜΑ ΤΩΝ ΤΡΙΩΝ ΣΩΜΑΤΩΝ

THE PERIODIC SOLUTIONS OF NON-INTEGRABLE DYNAMICAL SYSTEMS HAVE BEEN THE SUBJECT OF A GREAT DEAL OF RESEARCH, AND ARE OF PARTICULAR IMPORTANCE IN THE STUDY OF MECHANICAL SYSTEMS. A NON-INTEGRABLE DYNAMICAL SYSTEM CANNOT BE DESCRIBED BY ANALYTICAL METHODS AND NUMERICAL TREATMENT, WITH THE USE OF FAST COMPUTERS IS OFTEN NECESSARY. SUCH DYNAMICAL SYSTEMS ARE AMONG OTHERS, THE CLASSICAL "THREE BODY PROBLEM" AND ITS SIMPLIFIED VERSIONS KNOWN AS THE (CIRCULAR) "RESTRICTED THREE-BODY PROBLEM" AND THE "ELLIPTIC RESTRICTED THREE- BODY PROBLEM". THISTHESIS CONSISTS OF EIGHT CHAPTERS: IN CHAPTER 1 WE GIVE THE EQUATIONS OF MOTION OF THE THREE-DIMENSIONAL ELLIPTIC AND CIRCULAR THREE-BODY PROBLEM, THE POINTS OF EQUILIBRIUM, THE RECTILINEAR MOTION OF THE 2-AXIS, AND THE ANALYTICAL APPROXIMATIONS DESCRIBING THE MOTION IN THE NEIGHBOURHOOD OF AN EQUILIBRIUM POINT. IN CHAPTER 2 WE GIVE THE EQUATIONS OF VARIATION AND DISCUSS THE STABILITY OF PERIODIC SOLUTIONS, GENERALLY OR ISOENERGERICALLY, AS WELL AS THE SYMMETRY PROPERTIES OF THE SOLUTIONS. (SHORTENED)

Grantor dc:publisher

University of Patras

Year dc:date

1985

Author dc:creator

• Περδίος, Ευστάθιος

• ΑΣΤΑΘΗ ΣΗΜΕΙΑ ΙΣΟΡΡΟΠΙΑΣ
• Ασυμπτωτικές τροχιές
• ΔΙΑΚΛΑΔΩΣΕΙΣ ΟΙΚΟΓΕΝΕΙΑΚΩΝ ΠΕΡΙΟΔΙΚΩΝ ΤΡΟΧΙΩΝ
• ΕΥΣΤΑΘΕΙΑ ΠΕΡΙΟΔΙΚΩΝ ΤΡΟΧΙΩΝ
• Περιοδικές τροχιές
• ΣΕΙΡΕΣ ΚΡΙΣΙΜΩΝ ΠΕΡΙΟΔΙΚΩΝ ΤΡΟΧΙΩΝ
• Asymptotic orbits
• BIFURCATIONS OFFAMILY PERIODIC ORBITS
• Periodic orbits
• SERIES OF CRITICAL PERIODIC ORBITS
• STABILITY OF PERIODIC ORBITS
• UNSTABLE EQUILIBRIUM POINTS
• Φυσικές Επιστήμες
• Μαθηματικά
• Natural Sciences
• Mathematics

Language dc:language

gre

Identifier

10.12681/eadd/0594

OAI identifier oai:identifier

oai:10442/0594