A new integrable problem with a quartic integral in the dynamics of a rigid body

Abstract

We consider the problem of motion of a rigid body about a fixed point under the action of an axisymmetric combination of potential and gyroscopic forces. We introduce a new integrable case, valid on zero level of the cyclic integral, that generalizes the known case of motion of a body in liquid due to Chaplygin and its subsequent generalization by Yehia. Apart from certain singular potential terms, the new case involves finite potential and gyroscopic forces, which admit physical interpretation as resulting from interaction of mass, magnetized parts and electric charges on the body with gravitational, electric and magnetic fields.

This work will appear shortly in "Journal of Physics A: Mathematical and Theoretical"

References in corpus (1)

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

Cited by in corpus (5)

• Bäcklund transformations for the nonholonomic Veselova system
• Integrable discretization and deformation of the nonholonomic Chaplygin ball
• On two-dimensional integrable models with a cubic or quartic integral of motion
• New families of integrable two-dimensional systems with quartic second integrals
• Deformations of the Poisson brackets and the Kowalevski top