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a simple swinging pendulum plotted with respect to time.

The two near-sinusoidal

curves are out of phase since the peak joint velocity occurs when the joint angle is

zero and the peak angle occurs when the velocity is zero.

t

q

Figure A-1 - State vs time for a 1 degree-of-
freedom swinging pendulum plotted
vs time.

State space- The set of all possible values of the state of an object. A trajectory through the

state space of an object describes its motion.

representation of the trajectories of Figure A-1.

FigureA-2 shows the state space

Limit cycle- A periodic, cyclic trajectory through state space.

The trajectory in Figure A-2

is an example of a limit cycle which represents the periodic motion of a simple

pendulum.

Throughout this thesis, the term limit cycle is used to refer to cyclic,

periodic motion in part of the state space rather than strictly applying to the full state

space.

·

q

Figure A-2 - State-space trajectory of a simple
swinging pendulum.