# Re: Pendulum mechanics

Lee Daniel Crocker (lcrocker@calweb.com)
Sun, 20 Jul 1997 13:57:06 -0700 (PDT)

> > Body movements can alter one's center of gravity significantly. Just
> > as a high jumper can clear a bar without ever having his center of
> > gravity above it, the child on the swing can move his legs in or out,
> > and bend at the waist, to move his center of gravity just a touch
> > higher on each swing than the height attributable to the energy of
> > the previous reciprocal swing. On the downstroke, he repositions his
> > body again to prepare for the maneuver on the other side, which uses
> > the energy of his muscles without depleting any of the gravitational
> > potential energy he has gained. The amount of extra energy put into
> > the system from his own muscles is enough to escalate each swing.
>
> But what is the energy put into? If true action/reaction holds, the
> rider moving its center of gravity higher will only reduce the momentum
> at that point in the swing, so it will not move any higher. If true
> action/reaction holds, as it is popularly understood, the rider should
> not be able to gain any momentum on each swing without causing a
> reaction....

The energy is "put in" as gravitational potential. Imagine standing on
the swing. Through most of the stroke you crouch, but when you reach
the apex of the swing, you stand up. At that point, you have used to
muscles of your legs to raise your center of gravity above where the
swing put it. As you crouch again on the downswing, you will arrive a
little bit higher on the other side than you would if you hadn't done
that maneuver, and of course when you get there, you'll stand up again
adding yet more gravitational potential.