The thing I have never been able to grasp with the space elevator concept is how the cable(s) would be strung so that it isn't torqued/twisted by the Earth's rotation. Or is elevator's centripetal acceleration supposed to straighten it out?
Imagine in your brain a standard, boring geosync comsat. There it is, hovering over some spot of land in Africa or WTF, 24x7. (well, its not quite that simple, but close enough). Now take two jumpropes and throw one down and one up. No problemo its still "motionless" WRT the ground. Now make those jumpropes ridiculously long until suddenly the lower one hits the ground. There's never a point as it stretches where it gets all spun around and stuff.
You are tangentially correct in that its a huge dynamic problem to dampen waves. You wanna piss off / terrify legacy earthlings today? Get in an elevator with 500 foot cables and start hopping up and down while its moving. You'll scare them half to death as the whole cabin starts bouncing. Now try a couple thousand mile long cable with multiple cabins all wiggling. Its going to give the control system engineers headaches. Solvable, just a PITA.
The tether would extend far far out over a geosynchronous orbit, such that the centripetal acceleration is exactly equal to the force of gravity. Thus, it would be weightless on the ground, maximum tension at geosynchronous orbit, and an easy launching platform at its end.
Also, it can be easily deployed by unrolling the tether in both directions simultaneously from the geosynchronous orbit.
The tether actually extends out past geosynchronous orbit. The section below geosynchronous orbit want to fall to earth, and the section above wants to fly away. Because of this, the tether is under tension.
