New families of integrable two-dimensional systems with quartic second integrals

Abstract

The method introduced in (Yehia H M 2006 J. Phys. A: Math. Gen. 39 5807-5824) and (Yehia H M 2012 J. Phys. A: Math. Gen. 45 395209) is extended to construct new families of several-parameter integrable systems, which admit a complementary integral quartic in the velocities. A total of 12 new systems are obtained, with a number of parameters ranging from 7 up to 16 parameters.

References in corpus (1)

• Atlas of two-dimensional irreversible conservative lagrangian mechanical systems with a second quadratic integral

Cited by in corpus (2)

• On auto and hetero Backlund transformations for the Henon-Heiles systems
• On two-dimensional integrable models with a cubic or quartic integral of motion