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Riemann hypothesis should be next... Which paper on the linked website is this exactly?

hmmm, last year at the AIAA conference in Toronto I presented a continuation approach to design a DRO (three-body problem). Nothing new here unfortunately. I know the work of Caillau, although interesting what is presented was solved 10 years ago by others. The interest of his work is not in the applications (CR3BP), but in the research of particular regularity conditions that unfortunately make the problem limited practically. Look also at the work of Mingotti, Russel, Topputo and other for the (C)RTBP. Smart-One inspired a bunch of researchers :)

Topputo and some of the others 'inspired' researchers you mention are actually here at the conference and they are all quite depressed :) Caillau really solves the problem: as a one single phase transfer, no tricks, no misconvergence, in general and using none of the usual cheats. What was produced so far by other were only local solutions valid for the particular case considered. In any case I will give him your paper, so that he knows he is working on already solved stuff :)

Answer to Marek: the paper you may look at is: Discrete and differential homotopy in circular restricted three-body control

Ah! with one single phase and a first order method then it is amazing (but it is still just the very particular CRTBP case). The trick is however the homotopy map he selected! Why this one? Any conjugate point? Did I misunderstood the title ? I solved in one phase with second order methods for the less restrictive problem RTBP or simply 3-body... but as a strict answer to your title the problem has been solved before. Nota: In "Russell, R. P., "Primer Vector Theory Applied to Global Low-Thrust Trade Studies," JGCD, Vol. 30, No. 2", he does solve the RTBP with a first order method in one phase.

I think what is interesting is not what he solved, but how he solved the problem. But, are means more important than end ... I dunno

I also loved his method, and it looked to me that is far more general than the CRTBP. As for the title of this post, OK maybe it is an exageration as it suggests that no solution was ever given before, on the other end, as Marek would say "come on guys!!!!!"

The generality has to be checked. Don't you think his choice of mapping is too specific? he doesn't really demonstrate it works better than other. In addition, the minimum time choice make the problem very regular (i guess you've experienced that solving min time is much easier than mass max, optimality-wise). There is still a long way before maximum mass+RTBP, Topputo et al should be re-assured :p Did you give him my paper, he may find it interesting since I mention the homotopy on mu but for max mass:)

Joris, that is the point I was excited abut, at the conference HE DID present solutions to the maximum mass problem!! One phase, from LEO to an orbit around the moon .. amazing :) You will find his presentation on line.... (according to the organizers) I gave him the reference to you paper anyway, but no pdf though as you did not upload it on our web pages and I could not find it in the web. So I gave him some bibliography I had with be from the russians, and from Russell, Petropoulos and Howell, As far as I know these are the only ones that can hope to compete with this guy!!

for info only, my phd, in one phase: http://pdf.aiaa.org/preview/CDReadyMAST08_1856/PV2008_7363.pdf I prefered Mars than the dead rock Moon though!

If you send me the pdf I can give it to the guy .. the link you gave contains only the first page ... (I have no access till monday to the AIAA thingy)

this is why I like this Diigo thingy so much more than delicious ...

What do you mean by this comment, Leopold? ;-) Jokes apart: I am following the Diigo thingy with Google Reader (rss). Obviously, I am getting the new postings. But if someone later on adds a comment to a post, then I can miss it, because the rss doesn't get updated. Not that it's a big problem, but do you guys have a better solution for this? How are you following these comments? (I know that if you have commented an entry, then you get the later updates in email.) (For example, in google reader I can see only the first 5 comments in this entry.)

hmm, not very chaotic indeed - laws of Kepler plus some perturbations.

It's installed on my computer, but I never really used it. I think it's fine, but for my purposes latexdiff mostly is enough.

An energy scenario published by an oil company? Allow me to be sceptical...

Indeed, Shell is an energy company, not just oil, for some time now ... The two scenarii are, in their approach, dependant of economic and political situation, which is right now impossible to forecast. Reference to Kyoto is surprising, almost out-dated! But overall, I find it rather optimistic at some stages, and probably the timeline (p37-39) is unlikely with recent events.

the report was published in 2008, which explains the reference to Kyoto, as the follow-up to it was much more uncertain at that point. The Blueprint scenario is indeed optimistic, but also quite unlikely I'd say. I don't see humanity suddenly becoming so wise and coordinated. Sadly, I see something closer to the Scramble scenario as much more likely to occur.

not an oil company??? please have a look at the percentage of their revenues coming from oil and gas and then compare this with all their other energy activities together and you will see very quickly that it is only window dressing ... they are an oil and gas company ... and nothing more

not JUST oil. From a description: "Shell is a global group of energy and petrochemical companies." Of course revenues coming from oil are the biggest, the investment turnover on other energy sources is small for now. Knowing that most of their revenues is from an expendable source, to guarantee their future, they invest elsewhere. They have invested >1b$ in renewable energy, including biofuels. They had the largest wind power business among so-called "oil" companies. Oil only defines what they do "best". As a comparison, some time ago, Apple were selling only computers and now they sell phones. But I would not say Apple is just a phone company.

window dressing only ... e.g. Net cash from operating activities (pre-tax) in 2008: 70 Billion$ net income in 2008: 26 Billion revenues in 2008: 88 Billion Their investments and revenues in renewables don't even show up in their annual financial reports since probably they are under the heading of "marketing" which is already 1.7 Billion $ ... this is what they report on their investments: Capital investment, portfolio actions and business development Capital investment in 2009 was $24 billion. This represents a 26% decrease from 2008, which included over $8 billion in acquisitions, primarily relating to Duvernay Oil Corp. Capital investment included exploration expenditure of $4.5 billion (2008: $11.0 billion). In Abu Dhabi, Shell signed an agreement with Abu Dhabi National Oil Company to extend the GASCO joint venture for a further 20 years. In Australia, Shell and its partners took the final investment decision (FID) for the Gorgon LNG project (Shell share 25%). Gorgon will supply global gas markets to at least 2050, with a capacity of 15 million tonnes (100% basis) of LNG per year and a major carbon capture and storage scheme. Shell has announced a front-end engineering and design study for a floating LNG (FLNG) project, with the potential to deploy these facilities at the Prelude offshore gas discovery in Australia (Shell share 100%). In Australia, Shell confirmed that it has accepted Woodside Petroleum Ltd.'s entitlement offer of new shares at a total cost of $0.8 billion, maintaining its 34.27% share in the company; $0.4 billion was paid in 2009 with the remainder paid in 2010. In Bolivia and Brazil, Shell sold its share in a gas pipeline and in a thermoelectric power plant and its related assets for a total of around $100 million. In Canada, the Government of Alberta and the national government jointly announced their intent to contribute $0.8 billion of funding towards the Quest carbon capture and sequestration project. Quest, which is at the f

thanks for the info :) They still have their 50% share in the wind farm in Noordzee (you can see it from ESTEC on a clear day). Look for Shell International Renewables, other subsidiaries and joint-ventures. I guess, the report is about the oil branch. http://sustainabilityreport.shell.com/2009/servicepages/downloads/files/all_shell_sr09.pdf http://www.noordzeewind.nl/