A new linear invariant relation of the Poincaré–Zhukovskii equations

A new invariant relation of the Poincaré–Zhukovskii equations is described. The integration problem is reduced to solving the Riccati equation. The cases when the original Poincaré–Zhukovskii system has an additional linear integral and when such an integral exists for motion with a linear invariant relation are identified. ©2012.