  The flywheel ball and hexagonal structures in the design of the classical
centrifugal governor systems lead to both modeling and analytical difficulties.
In the present paper, a new trigonal centrifugal governor is proposed in an
attempt to overcome both of these difficulties by introducing the radical
nonlinearity and nonsmooth control strategy in the simple and clear formula.
The nonlinear dynamical behaviors of this new model are investigated for both
the autonomous and the non-autonomous cases. The three equations of motion of
the TCG are presented based on Euler-Lagrange equation and the theorem of
angular momentum. The velocity, nonlinear restoring force and nonsmooth torque
surfaces are plotted to display the complex relationship of parameter change
dependence. Secondely, the equilibrium bifurcation and stability analysis for
autonomous system are investigated to show the pitchork bifurcation phenomena
and the saddle-focus point respectively. It is found that the system bears
significant similarities to the Duffing system with mono-stable and bi-stable
characteristic. Finally, the three-dimensional Melnikov method is defined and
employed to obtained the analytical chaotic thresholds for non-autonomous
centrifugal governor system, and numerical results of chaotic behaviors verify
the proposed theoretical criteria of the non-autonomous system. The
experimental studies are carried out to validate the theoretical and numerical
results.
