The motion of a system close to Hamiltonian with one degree of freedom when there is resonance in forced vibrations

✍ Scribed by O.V. Kholostova

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 429 KB
• Volume: 60
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(96)00050-0

✦ Synopsis

The motion of an auto:aomous mechanical system with one degree of freedom subject to small time-periodic perturbations and small dissipative forces in the vicinity of a stable position of equilibrium of the system is considered. It is assumed that resonance occurs in forced vibrations when the ratio of the frequency of small vibrations of the system to the frequency of the external periodic perturbation is close to an integer. The qualitative behaviour of an approximate system is studied. Depending on the parameters of the problem, namely, the magnitude of the dissipation and resonance detuning, a rigorous solution of the problem of the existence, number, and stability of periodic motions (the period being equal to that of the perturbation) arising from the position of equilibrium of the unperturbed system is given. As an example the motion of a pendulum with oscillating point of suspension is considered.