Spatial chaotic vibrations when there is a periodic change in the position of the centre of mass of a body in the atmosphere

✍ Scribed by V.S. Aslanov

• Book ID: 104020708
• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 377 KB
• Volume: 73
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/j.jappmathmech.2009.04.007

✦ Synopsis

The spatial chaotic motion of a blunt body in the atmosphere when there is a periodic change in the position of the centre of mass is considered. A restoring moment, described by a biharmonic dependence on the spatial angle of attack, a small perturbing moment, due to the periodic change in the position of the centre of mass, and also a small damping moment, acts on the body. The motion when the velocity head remains constant is investigated. When there are no small perturbations, the phase portrait of the system can have points of stable and unstable equilibrium. The behaviour of the system in the neighbourhood of the separatrice is investigated using Mel'nikov's method. An analytic solution of the equation of the body motion along the separatrice is obtained. The criteria for the occurrence of chaos are obtained and the results of numerical modelling, which confirm the correctness of the solutions obtained, are presented.