Definitions of the inertial coordinate system and the noninertial coordinate system with origin at the pendulum's tip.
Trajectory of a lengthening pendulum where , with r in meters and t in seconds. Note both the lengthening and the decreasing angular amplitude.
Displacement angle vs. time for the trajectory depicted in Fig. 2 .
Trajectory of a lengthening pendulum over an extended period.
Depiction of the pendulum being pulled in at the bottom and let out at the high point of its cycle.
Plot of pendulum state variables over one oscillation period. The positions at which pulling-in and letting-out impulses are applied are displayed. In the top panel, the units of θ are such that at the low point and at either high point of the swing.
Comparison of the trajectories for different pulling and letting times, again using the convention where at the low point and at either high point of the swing. Pulling near the bottom (0.05) and letting near the top (0.95) can strongly increase the amplitude.
(Color online) Normalized energy after 300 s as a function of pulling-in and letting-out impulse positions. Note the strong peak when pulling at the bottom and letting at the high points of each cycle.
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