Abstract
We consider a controlled mechanical system with one degree of freedom described by an angular coordinate. The system is under the action of conservative and nonconservative forces. It is assumed that a corresponding dynamic system has a variable parameter that describes the control-impact gain factor. An iterative numerical–analytical method designed to form autorotation modes with assigned properties is proposed. The conditions for the orbital stability of such modes are formulated. The proposed approach represents a modification of the Andronov–Pontryagin method and, as opposed to it, can be applied not only to systems close to Hamiltonian systems but also to a certain class of systems that do not contain a small parameter. An example of the method’s application to an aerodynamic pendulum model is presented. The ability to expand the method’s convergence domain by using the parameter-continuation procedure is demonstrated.
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