If you find this stuff as fascinating as I do, I know of no better way to geek out about orbital mechanics than to play Kerbal Space program. Ex-NASA people quip that they learn more playing that than actually working at NASA.
It doesn't have multibody physics needed for ITN, but you'll learn tons of crazy things about the technicalities of space travel without realizing you've learned them.
That includes the realization that there are indeed ways to cross the universe using zero fuel. Also, you can burn towards a body to delay your arrival there. It's crazy, but the math checks out.
I worked on this for my Masters thesis [1], studying the nature of low-energy transfers [2] to the Moon, using the Weak Stability Boundary (WSB) [3]. Turns out that the WSB and invariant manifolds described by Dynamical Systems Theory (DST) [4] in the N-Body problem [5] are intricately linked. There was a bit of a "war" going on when I was doing my thesis between the group at Caltech that pioneered the (DST) methods, including people like Wang-Sang Koon, Shane Ross, and Martin Lo, and Ed Belbruno, who formalized the concept of the WSB, because there was still an evolving view of chaos in the gravitational 3-body problem.
It's a fascinating area of research that has implications for planetary formation and has been exploited for space mission design. I'm currently finalizing a paper that draws attention to the fact that low-energy orbits are likely an important component of a peculiar ring system around Uranus: the mu-ring/Mab system. Mab [6] shows strange orbital behavior that's likely intimately tied to interactions with a belt of moonlets that display horseshoe-like motion.
There's been some interesting research using the concept of orbital cyclers and the coincidental proximity of Lagrange points in the Earth-Sun and Mars-Sun systems. The only issue is that these orbits are necessarily very slow, so they're not suitable for time-critical applications.
This work occupies an odd niche that piques my curiosity. I knew Ed Belbruno slightly, and I'm cordial with Martin Lo. I'm trying to figure out how to say this neutrally: the people like the ones I mentioned do not seem to have much influence on the actual world of mission trajectory design. They're off on their own.
Yet when I read the summaries of their methods, they don't discuss any drawbacks besides the large transit times required. I'm left thinking that either there is something political/historical going on that I don't know about, or that the large times in fact totally kill the idea, rendering the theory moot. Come to think of it, another option is that reducing delta-v to zero is not worth going to so much trouble over (from a mission design viewpoint).
On the other hand, the scientific angle (that these trajectories can allow long-range mass circulation in the solar system) is very interesting and something I was not aware of. Thanks for your interesting reply.
It has occupied an odd niche in my curiosity ever since my first grad-level class in astrodynamics/celestial mechanics :) . It's a fascinating problem because it's inherently tied to many physical phenomena in our Solar System and in other planetary systems, yet the statement of the 3-body problem is pretty much as simple as it gets.
And you're right, they are kinda off on their own, but that's mostly because this niche is an interesting meeting of the minds for mathematicians, astrophysicists and engineers. That means you get some "interesting" discussions to say the least.
As for the "political/historical" aspects, have a chat with Ed sometime if you get the chance. He's got an interesting backstory that's catalogued in his books too. Basically, to some extent, there was a lot of resistance at JPL to his ideas, and so he had to bypass them, which is what brought about the Hiten mission.
As an objective researcher, I can say that low-energy transfers for mission design are interesting, but really for a specific subset of scenarios. Time-critical missions, e.g. manned spaceflight, falls outside the scope of low-energy transfers. Additionally, it turns out that the maths is a bit finicky and that low-energy transfers only lead to a significant Delta-V reduction if you launch in the right "geometry". In the case of Earth-Moon transfers for instance, it turns out that if you neglect the Sun, you can't actually reach the Moon "for free", as is advertised by WSB transfers, because of KAM tori around the Moon. The Sun is crucial, as it's perturbing effect ensures that phase-space opens up and you can actually reach the Moon. This comes with a BIG caveat though that the geometry of the Earth-Moon-Sun has to meet certain requirements. Hence, launch windows are limited.
As you point out, I do think the greater interest in studying low-energy orbits, WSB and invariant manifolds in high-order gravitational problems is in using the theory to explain natural processes. This fits within the larger context of dealing with resonances in the 3-body problem. Murray and Dermott have an excellent textbook on the fundamental theory behind all of this [1]. It's a must-buy if you're interested in delving into this further.
All of this has tremendous potential to elucidate exoplanet systems. There are plenty of systems discovered by Kepler, CoRoT etc. that require a deep, fundamental understanding of the processes that shape(d) them.
The pink/purple ones bounce between the L3, L4 and L5 points. The green ones are in orbits of the L4 or L5 points and have an orbital period that should be the same as jupiter itself.
The sci-fi technology that will truly enable mankind to efficiently explore space isn't fusion rockets, or space elevators, or any other grandiose machinery- its cryogenic sleep, or hibernation, or otherwise the ability to just conk out for long periods of time and wake up at your destination. Getting places in space is relatively easy, if you don't mind taking next-to-forever to get there. (In addition to the ITN, consider the bi-elliptic transfer: http://en.wikipedia.org/wiki/Bi-elliptic_transfer .)
"if you don't mind taking next-to-forever to get there."
If you want to be a (permanent-ish) space colonist that isn't wasted time.
As a counter example its continually proposed as a training / colonization system on short hops. If you want to test your 12-year rated life support system for a run to Jupiter, rather than sitting in low earth orbit the whole 12 years (boring!), why not try a leisurely ITN flight to the moon, in fact why not leave the ship/station in moon orbit when you're done, as a moon orbiting station?
If something goes horribly wrong, keep some large delta-v chemically fueled beast of a lifeboat around, worst case scenario on your "12 year mission to the moon" you'll never be more than many hours (well, OK, days worst case) from a splashdown on the earth via a very non-ITN path. Also your giant station/ship could be resupplied from the earth, at a considerably higher than ITN cost. Given your station/ship can move orbits very cheaply, your "lifeboat" could be extremely high performance.
The ITN would be a great way to help a manned (anywhere) expedition by slowly sending enormous quantities of cargo and base equipment long ahead of time.
A group that plans for the future would probably already be planning care packages and emergency packages to likely destinations. If it takes people 20 years to get to eventually really quickly fly to mars, then its no big deal if emergency O2 and first aid kits or whatever launched today take perhaps 15 years in transit.
But we do mind - unless we develop a cure for aging, there's no point in sending anyone anywhere if they're going to travel 50 years or more. By then, we'll lose interest in any data or resources we wanted.
Considering the very large distances, I suppose it would require very little in the way of manual intervention or energy. But I wonder how safe it will be unless at least one or two crew members are left awake to attend to the rest in case of emergencies.
That also leaves the question of what method to use for hibernation. Many mammals already do, but we may require a drastic change in our physiology or dive into genetic engineering (without knowing long-term effects, it could be dangerous) or discover some substance to inject into our blood or replace it altogether so we may lower our metabolism.
I'm still a fan of the Aldrin Cycler. Put an utterly massive, nearly self-sufficient space station into an orbit that touches both Mars and Earth (or presumably other pairs). Give it all the radiation shielding and spinning gravity you'd need to survive indefinitely in space. Now your per trip cost is just getting the astronauts to and from the surfaces of each planet.
From December 17, 1903 to present day, a large number of people have died while we were still trying to improve air travel for everyone. Their deaths were tragic, but their contribution to modern aviation and the betterment of our civilization as a result is incalculable.
Space travel will likely have a similar high price. The long-term survival of our species depends on the success of those who try regardless.
It doesn't have multibody physics needed for ITN, but you'll learn tons of crazy things about the technicalities of space travel without realizing you've learned them.
That includes the realization that there are indeed ways to cross the universe using zero fuel. Also, you can burn towards a body to delay your arrival there. It's crazy, but the math checks out.