As Mike Scott mentions, Sheffields book The Web Between the Worlds fits the bill. Here is the relevant passages, as gleaned from amazon's "look inside" feature:
..if we send a mass all the way to the end of the beanstalk, far beyond geostationary orbit, the we will also have a free launch system. A mass released from 100,000 kilometers out can be thrown to any part of the solar system. The energy for this is, incidentally, free. It is provided by the rotational energy of the Earth itself
since any energy used in the drive train to take mass up the beanstalk can be recovered by making the same mass do work as it comes down, a remarkably efficient system is possible. And by using the beanstalk as a slingshot, we have the energy-free launch system for payloads going to destinations anywhere in the solar system
But note that this is from the book's second appendix, "space elevators in fact and fiction" where the author goes into technical detail. I'm not sure if it's elaborated on in-story or if the appendix was present in the first edition. In any case, and with apologies to Heinlein, there is no such thing as a free launch.