الفهرس 
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Abstract
Over the past thirty years there has been a wide spread interest in the phenomena of chaos and strange attractors. Many researchers in the fields of mechanics, physics, chemistry, biological, economical and social sciences have vigorously inve.stigated.
The main objective of this thesis is intended to give a general review of chaos, the idea behind the transitions to chaotic solutions for dynamical systems and finally we investigate the rotating pendulum and rotating beam.
The review is presented to serve the readers who are not familiar with the terminology of chaos. In the review a little historical background about the work done on the chaotic motion is given. Time series, phase portrait, Poincare maps and power spectrum for some examples to recognize chaotic motion is discussed. Also the properties of chaotic motion, like, sensitivity to initial conditions, Lyapunov exponent and the dimension function are discussed.
The idea behind transitions to chaotic solutions such as the period-doubling cascade, intermittency, crises, homoclinic and heteroclinic bifurcation, and quasiperiodic routes to chaos are discussed. Some of these transitions, such as the period-doubling sequence are associated with local bifurcations, while the other transitions are associated with global bifurcations.
Mathematically, the rotating pendulum is modeled by a differential equation possess¬ing sine and cosine nonlinearities. The system is autonomous with both homoclinic and heteroclinic orbits at zero damping coefficient and zero exciting force. The homo clinic and heteroclinic orbits are calculated. For both orbits a direct calculation of the Melnikov functions proves the existence of chaos for sufficiently large amplitude of the excitation force.