摘要：On the basis of controlled Lagrangians,a controller design is proposed for underactuated mechanical systems with two degrees of freedom.A new kinetic energy equation(K-equation)independent of the gyroscopic forces is found due to the use of their *** a result,the necessary and sufficient matching condition comprises the new K-equation and the potential energy equation(P-equation)cascaded,the regular condition,and the explicit gyroscopic ***,for two classes of input decoupled systems that cover the main benchmark examples,the new K-equation,respectively,degenerates from a quasilinear partial differential equation(PDE)into an ordinary differential equation(ODE)under some choice and into a homogeneous linear PDE with two kinds of explicit general *** from one of the general solutions,the obtained smooth state feedback controller for the Acrobots is of a more general ***,a constant fixed in a related paper by the system parameters is converted into a controller parameter ranging over an open interval along with some new nonlinear terms *** what is mentioned in the related paper,some categories of the Acrobots cannot be stabilized with the existing interconnection and damping assignment passivity based control(IDA-PBC)*** a contribution,the system can be locally asymptotically stabilized by the selection of the new controller parameter except for only one special case.