The influence of dissipative and constant forces on the form and stability of steady motions of mechanical systems with cyclic coordinates

✍ Scribed by A.V Karapetyan; I.S Lagutina

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 534 KB
• Volume: 62
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(98)00066-5

✦ Synopsis

Mechanical systems with cyclic coordinates subject to dissipative forces with complete dissipation and constant forces applied only to the cyclic variables are considered. Problems of the existence of steady motions in such systems and the conditions for their stability are discussed. It is shown, in particular, that if the Rayleigh function is proportional to the kinetic energy, the stability conditions for the steady motions of the system are the same as or (under certain assumptions) similar to such conditions for steady motions of a corresponding conservative system. The example of a physical pendulum is used to show that such conclusions are generally false: dissipative and constant forces may cause destabilization of stable motions of the system.