Open AccessDETERMINATION OF THE STABILITY BOUNDARIES FOR THE HAMILTONIAN SYSTEMS WITH PERIODIC COEFFICIENTS
Author(s) -
Alexander N. Prokopenya
Publication year - 2005
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2005.9637281
Subject(s) - hamiltonian system , mathematics , computation , hamiltonian (control theory) , ordinary differential equation , symbolic computation , stability (learning theory) , instability , mathematical analysis , differential equation , physics , algorithm , computer science , mathematical optimization , machine learning , mechanics
We consider the hamiltonian system of linear differential equations with periodic coefficients. Using the infinite determinant method based on the existence of periodic solutions on the boundaries between the domains of stability and instability in the parameter space we have developed the algorithm for analytical computation of the stability boundaries. The algorithm has been realized for the second and the fourth order hamiltonian systems arising in the restricted many-body problems. The stability boundaries have been found in the form of powers series, accurate to the sixth order in a small parameter. All the computations are done with the computer algebra system Mathematica.Nagrinejama Hamiltono tiesiniu diferencialiniu lygčiu su periodiniais koeficientais sistema. Remiantis tuo, kad parametru erdveje stabilumo ir nestabilumo sritis skiriančioje sienoje egzistuoja periodinis sprendinys, sukurtas analitinis minetos sienos apskaičiavimo algoritmas. Algoritmas realizuotas antros ir ketvirtos eiles Hamiltono sistemoms, kylančioms nagrinejant apribotu keleto kūnu uždavinius. Stabilumo srities siena randama laipsnines eilutes pavidalu mažojo parametro šešto laipsnio tikslumu. Skaičiavimai atlikti skaičiavimo algebros paketo Mathematica pagalba.