The paper considers two new integrable systems due to Chaplygin, which describe the rolling of a spherical shell on a plane, with a ball or Lagrange’s gyroscope inside. All necessary first integrals and an invariant measure are found. The reduction to quadratures is given.
Keywords:
non-holonomic constraint, integrability, invariant measure, gyroscope, quadrature, coupled rigid bodies
Citation:
Borisov A. V., Mamaev I. S., Two non-holonomic integrable systems of coupled rigid bodies, Rus. J. Nonlin. Dyn.,
2011, Vol. 7, No. 3,
pp. 559-568
DOI:10.20537/nd1103011