Optimal control of motions of a bifilar pendulum

✍ Scribed by L.D. Akulenko

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 859 KB
• Volume: 68
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/j.jappmathmech.2004.09.007

✦ Synopsis

The controlled oscillatory and rotational motions of a rigid body on a plane-parallel bifilar suspension are investigated. The controlled object, the relative position of which can be regulated, is connected to the body. The vectors of the acceleration or the rate of displacement of the object with respect to the body. The vectors of the acceleration or the rate of displacement of the object with respect to the body are used as the control functions. The values of the control functions are assumed to be small compared with the gravitational forces, which enables a small parameter to be introduced into the dimensionless variables. Specific regions of constraints (a rectangle, ellipse, or an inclined segment) are considered. Using asymptotic methods, a solution of the first approximation is constructed for the problem of the optimal control of the oscillation and rotation energies of the system. The case of small oscillations and fast rotations are investigated separately. The qualitative features of the controlled motions of a bifilar pendulum are established and commented on.