I just read a brief but excellent 2007 book called Fly Me to the Moon (subtitled "an insider's guide to the new science of space travel") by Edward Belruno. Here's a review I just posted to Amazon:
Mathematics, orbital mechanics, chaos theory - is this the stuff of a good read for anyone other than a physicist, astronomer, or JPL engineer? Surprisingly enough, yes. This small book tells the story of how an interesting but subtle and specialized idea was developed and ultimately applied to real space missions. The idea is to make use of the interactions of the gravitational fields of (say) the Earth and the Moon to determine high-efficiency trajectories, e.g., to design a trajectory from the Earth to the Moon that uses very little fuel compared to normal methods (e.g., Hohmann transfer orbits).
When the author first started experimenting with these trajectories, he met with skepticism from space flight experts at JPL, where he was working at the time. Part of this skepticism came from the verbal implications of "chaos theory," which implies unpredictability or randomness, something you don't want in a space probe's trajectory! But in this context, chaos theory really just means that certain paths are very sensitive to small changes, meaning that small forces can cause big changes in the path. Although there are not exact equations for these multi-body gravity problems, they can be accurately simulated on computers. When the method was successfully applied to helping a Japanese space probe (Hiten) get to the Moon in 1991 using very little fuel (ironically just as the author was leaving JPL), it started to get serious attention, and has since been used for several successful missions. The efficiency of these trajectories will be useful in future missions to the Moon and planets, and the method could also help us to predict the trajectories of asteroids and comets that may threaten Earth.
This review is probably more technical than the book! Despite the specialized subject matter, the author uses clear, simple descriptions and analogies along with hand-drawn sketches of the various paths as he unfolds the implications and applications of the method. It's one of those books like Longitude (Sobel) or Roving Mars (Squyres) that puts you inside the head of someone who is very passionate about their work, allowing you to look over their shoulder, as it were, and understand why someone would be fascinated by this stuff, as well as what it all means.
I am a dabbler in simulated space flight using the free program Orbiter, and I know a bit about orbital mechanics and how hard it can be to explain something so seemingly obscure to non-specialists, as I often do in presentations as a volunteer educator in JPL's Solar System Ambassador program. So I really appreciate the excellent way the author presents this subject, and I will recommend the book to anyone with curiosity about space or astronomy.
If you are interested in playing around with orbits yourself, without using mathematics, Orbiter is one good possibility, but a better bet might be Gravity Simulator 2.0, which is also free. Orbiter is focused on navigating and flying the spacecraft, while Gravity Simulator shows you animated orbit diagrams. Although I don't see any examples of Dr. Belbruno's work in the supplied samples, this program can simulate very complex orbits and I believe it would be possible to simulate some of the cases described in the book.