13141

11991

كارشناسي ارشد

طراحي كاربردي

اصفهان: دنشگاه صنعتي اصفهان، دانشكده علوم رياضي

۱۳۹۶

ده، [۱۴۴]ص.: مصور، جدول

رضا مزروعي سبداني

رضا خوش سير، مجيد گازر

1396/11/03

كتابنامه

علوم رياضي

رياضي

ID11991

Integrability and Non integrability of Hamiltonian Normal Forms and Perturbations of Superintegrable Systems Masoud Khodadadi khodadadi@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Mazrooei Sebdani mazrooei@cc iut ac ir 2010 MSC 37J15 37J35 37J40 37J45 37J99 Keywords Hamiltonian systems Normal forms Non integrability Hamiltonian chains Time series Superintegrable system AbstractThe evolution of physics after the emergence of classical mechanics and Lagrangian mechanics cameto a new formulation of the Hamiltonian mechanics and provided the ground for the emergenceof quantum mechanics in the late nineteenth century In 1834 Hamilton described the differentialequations of classical mechanics In fact in this new form of classical mechanics it was possible toobtain particle motion equations regardless of the forces exerted on the particles in a system and thecomplex geometry governing some systems Hamilton expressed the differential equations of classical mechanics the Lagrange equations d L L L Rn Rn R dt q q in the canonical form H H p q p q Rn is the generalized momentum and the Hamiltonian function H pq L p q is the LHere p q total energy of the mechanical system Many natural phenomena become Hamiltonian function after modeling Hamiltonian functions todayare one of the most widely used models in engineering and physics Therefore studying the Hamilto nian functions and consequently the systems derived from these functions the Hamiltonian systems and the study of how to obtain the solutions of these systems is important The problem of integration of Hamiltonian systems had already been discussed in works of the brothers

رضا مزروعي سبداني

رضا خوش سير، مجيد گازر