Olya V. EFIMOVSKAYA
Department of Mechanics and Mathematics,
Moscow State University,
Vorob'evy gory, Moscow, 119992, RUSSIA
E-mail: efvitaly@ttk.ru

Quadratic Hamiltonians on e(3) with 3rd and 4th degree first integrals

Abstract:
Linear Poisson brackets on e(3) typical of rigid body dynamics are considered. All quadratic Hamiltonians of Kowalevski type having additional first integral of third and fourth degree are found. Quantum analogs of these Hamiltonians are listed. Computer Algebra techniques to solve large systems of conditions are discussed.