New 2D integrable families with a quartic second invariant

• Видавець: Інститут прикладної математики і механіки НАН України
• Дата: 2011
• Автор: Yehia, H.M.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут прикладної математики і механіки НАН України 2011
• Назва видання: Механика твердого тела
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/71597
• Цитувати: New 2D integrable families with a quartic second invariant / H.M. Yehia // Механика твердого тела: Межвед. сб. науч. тр. — 2011. — Вип 41. — С. 233-243. — Бібліогр.: 20 назв. — англ.

The method introduced by the present author in 1986 still proves most effective in constructing integrable 2-D Lagrangian systems, which admit in addition to the energy another integral of motion that is polynomial in velocities. In a previous article (J. Phys. A: Math. Gen., 39, 5807– 5824, 2006) we constructed a system, which admits a quartic complementary integral. This system, called by us “master”, is the largest known, as it involves 21 parameters, and contains, as special cases of it, almost all previously known systems of the same type that admit a quartic integral. In the present note we generalize the method we used before to construct new severalparameter systems that are not special cases of the master system. A new system involving 16 parameters is introduced and a special case of it admits interpretation in a problem of rigid body dynamics. It gives a unification of certain special versions of known classical integrable cases due to Kovalevskaya, Chaplygin and Goriatchev and other cases recently introduced by the present author.