pendulum

pendulum - The Nonlinear Pendulum The nonlinear pendulum...

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The Nonlinear Pendulum The nonlinear pendulum equation is θ ′′ = g l sin θ γθ , where θ is the angle that the pendulum makes from a downward vertical axis, measured counterclockwise; g is the gravitational constant, l the length of the pendulum, and γ is a damping constant, here measured (MKS units) in sec 1 . We take g/l = 1 for simplicity and set x = θ , y = θ , so we are studying the nonlinear system x = y y = sin x γy.
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Since x = θ is an angle, two points in the phase plane of the form ( x, y ) and ( x + 2 nπ, y ) represent the same physical point. Here are the equations again: x = y y = sin x γy. The system has critical points at x = , y = 0, where If n is even then the pendulum is motionless, hanging down;
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This note was uploaded on 09/29/2009 for the course 642 527 taught by Professor Speer during the Fall '07 term at Rutgers.

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pendulum - The Nonlinear Pendulum The nonlinear pendulum...

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