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LSU Doctoral Dissertations

Stability

2012

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Stability Problems In Constrained Pendulum Systems And Time-Delayed Systems, Prashanth Ramachandran Jan 2012

Stability Problems In Constrained Pendulum Systems And Time-Delayed Systems, Prashanth Ramachandran

LSU Doctoral Dissertations

In this dissertation, we study the boundary of stability of a class of linear mechanical systems as a function of a parameter. We consider two different systems under this class: a constrained double pendulum connected by a rigid rod and a state-feedback-controlled mechanical system with time delay. In the first system, the destabilizing parameter is the distance between the supports of the two pendulums. In the second system, the destabilizing parameter is the time delay. In the constrained double pendulum system, linear perturbation analysis is used to determine the natural frequency of the system. Our analysis reveals a zone of ...