The paper considers two new integrable systems which go back to Chaplygin. The systems consist of a spherical shell that rolls on a plane; within the shell there is a ball or Lagrange’s gyroscope. All necessary first integrals and an invariant measure are found. The solutions are shown to be expressed in terms of quadratures.
Keywords:
non-holonomic constraint, integrability, invariant measure, gyroscope, quadrature, coupled rigid bodies
Citation:
Borisov A. V., Mamaev I. S., Two Non-holonomic Integrable Problems Tracing Back to Chaplygin, Regular and Chaotic Dynamics,
2012, Volume 17, Number 2,
pp. 191-198