The equations of motion of a highly idealised model of a helicopter with a simple lag-hinged rotor are derived by Lagrange’s method. It is shown that the transformed equations governing Coleman instability (ground resonance) have a regular form involving wholly symmetric and skew-symmetric matrices. The work input to the unstable motions derives wholly from the torque applied to the rotor by the engine, but the torque equation is superfluous as far as the eigenvalues are concerned. Approximate stability criteria show that chassis and lag dampings per se are destabilising relative to the undamped reference condition and can lead to a substantial lowering of the critical rotor speed for instability onset. A necessary condition for instability (dynamic) is that two eigenvalues of the stiffness matrix are simultaneously negative.