الفهرس 
Survey of some perturbation techniques
On the motion of auto-parametric pendulumOnly 14 pages are availabe for public view
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Abstract
Chapter (1) presents a survey for useful perturbation techniques, like the straightforward expansion, Lindstedt-Poincaré technique, averaging method and multiple scales method. These In chapter (2), a modification model consists of mass M attached with damped spring and connected with a rigid arm of mass m is investigated. An external force F acting at the other end of the arm is considered. The multiple scales (MS) method is utilized to achieve the analytical solutions up to second approximation. In chapter (3), the problem of the response of a harmonically excited spring pendulum moving in elliptic path is investigated. The governing equations are established in framework of Lagrange’s equations. Applying MS method, these equations are solved analytically up to the third-order approximation. Moreover,all possible resonance cases are extracted at this approximation and analyzed numerically.