We study the problem of perturbations of quasiperiodic motions on coisotropic invariant tori in a class of locally Hamiltonian systems. We prove a general KAM-theorem on the perturbation of coisotropic invariant tori for locally Hamiltonian systems. As applications of this theorem, we consider the motion of an electron on a two-dimensional torus under the action of an electromagnetic field and extend results concerning the bifurcation of a Cantor set of coisotropic invariant tori to the case of locally Hamiltonian systems.
We study the bifurcation problem for a Cantor set of coisotropic invariant tori in the case where a Liouville-integrable Hamiltonian system undergoes locally Hamiltonian perturbations and, simultaneously, a deformation of the symplectic structure of the phase space. We consider a new case where the deformed symplectic structure generates a nondegenerate matrix of the Poisson brackets of action variables.
We study the problem of perturbations of quasiperiodic motions in the class of locally Hamiltonian systems. By using methods of the KAM-theory, we prove a theorem on the existence of invariant tori of locally Hamiltonian systems close to conditionally integrable systems. On the basis of this theorem, we investigate the bifurcation of a Cantor set of invariant tori in the case where a Liouville-integrable system is perturbed by a locally Hamiltonian vector field and, simultaneously, the symplectic structure of the phase space is deformed.
The task of this paper is to research the simultaneous use of trolley and hoisting mechanism by the tower crane with a beam jib. To conduct research, a dynamic model of joint movement of mechanisms has been developed, which takes into account the main movement of drive mechanisms and oscillating movement of the load on a flexible suspension and links of mechanisms with elastic properties. A mathematical model of the motion of mechanisms is constructed on the basis of a dynamic model with the help of Lagrange equations of the second kind. For a specific jib system of the tower crane, dynamic calculations were performed using the developed mathematical model. According to the results of the calculations, a dynamic analysis of the joint movement of trolley and hoisting mechanism was carried out. The analysis revealed significant dynamic and energy overloads of mechanisms during transients (start, braking) and the presence of high-frequency oscillations in the links with elastic properties and low-frequency oscillations of the load on a flexible suspension.
To reduce the overload of crane mechanisms in the areas of transients and eliminate oscillations during steady traffic, it is recommended to optimize traffic modes and develop drive control systems to implement the desired traffic modes.
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