Quote from: mmeijeri on 07/26/2009 12:59 amAnyone interested in an online study group for this?I am.

Anyone interested in an online study group for this?

Quote from: Hop_David on 07/27/2009 03:41 pmQuote from: mmeijeri on 07/26/2009 12:59 amAnyone interested in an online study group for this?I am.This thread is for a study group for the following online book: Dynamical Systems, the Three-Body Problem, and Space Mission Design by Koon, Lo, Marsden, and Ross. Discussion of the mathematics and physics involved as well as the applications to alternative exploration architectures are on topic for this thread.

Now I had thought kinetic energy was 1/2 * m * v^2

Yikes, typing those formulas into the editor is a lot of work!

I wish I had a head for this. Instead I am good with boolean and electronics systems. But it is a very good read none the less.

I put up a CR3BP model

The massless orbits in my CR3BP simulation don't remain in the Hill Region. They either drop to olive shaped orbits about the sun or they orbit about Jupiter making a big doughnut. They seem to drift into either the Sun or Jupiter realm. (as the authors call regions in Figure 1.2.3)

Quote from: Downix on 08/01/2009 05:53 pmI wish I had a head for this. Instead I am good with boolean and electronics systems. But it is a very good read none the less.How do you think I feel? I graduated in the upper 60% of my high school class and majored in art during my short time at a university. An obsession with M.C. Escher led me to a math hobby. I've learned much of the math and physics I know from the internet, library books and books purchased at yard sales. I often feel like a non-swimmer in the middle of a deep lake.Rummaging in my shed for helpful books I discovered Vector Calculus third edition by Jerrold E. Marsden and Anthony J. Tromba. Jerrold Marsden is one of the co-authors of the pdf Mmeijeri has linked to! I wonder if Jerrold is related to Brian Marsden of the Minor Planet Center.

David, could you put the required classes in your web directory? I think they may be in your class path on your own system, but I can't find them from here.

The trick is to update the positions first and then use the updated positions in the calculation of the forces and use that for updating the velocities:x_n+1 = x_n + v_x * dty_n+1 = y_n + v_y * dta_x_n+1 = F_x(x_n+1,y_n+1)/ma_y_n+1 = F_y(x_n+1,y_n+1)/mv_x_n+1 = v_x_n + a_x_n+1 * dtv_y_n+1 = v_y_n + a_y_n+1 * dt

He suggested I get the acceleration at the midpoint of the line segment connecting (xn, yn) and (xn+1, yn+1). He said this was a second order Runge Kutta integrator.

I recall making a 2 body model with a spread sheet using the above. Instead of an ellipse, I got a slowly growing spiral. Which is sort of what I expected since I knew I was piecing together a multitude of small parabola fragments. Jorge Frank told me I was using a first order Euler integrator.

Checked with my ftp program. orb.jar is in the railroad folder on clowder.net/hop/railroad. Ran the page from my co-worker's computer and it worked OK.

Quote from: Hop_David on 08/02/2009 09:32 pmChecked with my ftp program. orb.jar is in the railroad folder on clowder.net/hop/railroad. Ran the page from my co-worker's computer and it worked OK.When I try to log in on ftp://clowder.net I can get a dir listing, but all I see is directories bin, etc, incoming, lib, pub, with only incoming having any files in it. When I tried using Windows Explorer, it crashed! I'm logging in as anonymous.

Quote from: Hop_David on 07/29/2009 02:59 pmNow I had thought kinetic energy was 1/2 * m * v^2They are using a rotating frame with origin at the center of mass. They are also assuming the primaries move in perfectly circular orbits around the center of mass, as opposed to the more general case of elliptical orbits. Let A(t) be the 2x2 matrix defining the transformation from the moving frame with respect to an inertial reference system in the joint orbital plane with the origin at the center of mass, then we have:A(t) = R(omega * t),with R(theta) the 2x2 rotation matrix for a counterclockwise rotation through an angle theta and omega the angular velocity of the rotating frame. The rotating coordinates can then be described as a function of the inertial coordinates as follows:r^{~} = A * rwith r being the position vector in the inertial system and r^{~} the one in the rotating frame.Equivalently,r = A^{-1} * r^{~}Differentiating we getr = A^{-1}' * r^{~} + A^{-1} * r^{~}'by the product rule for differentiation. The first term on the left gives you the additional terms.. . .

I can download the jar, but somehow my JVM is not finding the .class file. Are all necessary class files inside the jar?

OK, it works for me now. I had to download the html and jar separately and open the html from disk and then it worked. It may have something to do with the HTML applet tag being deprecated. Could you try replacing the applet tag with the object tag on your web page?<object CLASSID="java:Orbit.class" archive="orb.jar" height="900" width="900">... params here ...</object>

When µ<<1, it's easy to set Jupiter's velocity so orbit is close to circular. But as µ becomes an appreciable fraction of 1, orbits become noticeably elliptical. I don't know how to set Jupiter's velocity so orbit is circular.

{snip}One interesting thing I saw: the L1 & L2 points are only about 6 kilometers above the surface of Phobos and 17 kilometers above the surface of Deimos. Building a Clarke tower from the Martian moons' surface to beyond the L1 and 2 points would be far more doable than other Clarke towers I've seen described. Don't know how useful these towers would be though.

You gotta let it evolve for a while... I got two (red and blue) in semi-stable orbits around the secondary body, and the rest ejected...Simon

This simulation result is great! Related questions: is it fair to characterize the delta-v needed to go from L1 to anywhere in the region painted by the red and blue objects as "trivially" low?

Does this region include Mars and the asteroids? Is this a strictly 2-D sim, and how careful need we be extrapolating results to 3-D?

On a topic related to L1 but not low-delta-v trajectories: is it fair to characterize EML1 as a "launch site neutral" destination, i.e. is the delta-v to reach EML1 from any terrestrial launch site the same?

Has anyone considered lunar gravity assists during, say, TMI?

I wanted to make sure the Parker paper on ballistic lunar transfers (BLT) was linked into this thread:http://ccar.colorado.edu/nag/papers/AAS%2006-132.pdfAlso a question about this: Parker calculates transfers that start in a 185-km LEO parking orbit. But realistically for many BLT missions the vehicle might be sent onto the outbound trajectory directly from launch, i.e. without making orbit first. Parker discusses departure delta-v values as low as 3210 m/s. The Atlas mission planner's guide provides charts showing payload capability depending on vis-viva energy (C_{3}). I'd like to make these match up. So what is the vis-viva energy for the departure trajectory Parker describes?

Very interesting stuff! A path that takes only 3.235 km/sec to get from a very low earth orbit to an EML2 halo orbit is an eye opener for me.

Quote from: sdsds on 08/24/2009 07:10 pmThis simulation result is great! Related questions: is it fair to characterize the delta-v needed to go from L1 to anywhere in the region painted by the red and blue objects as "trivially" low?All the diverging paths started off with very close velocities. At L1 a tiny nudge can result in a very different trajectory.Above is 3 realms the authors like to talk about. They're connected by "necks" at the L1 and L2. They talk about the comet Oterma which will orbit outside Jupiter's orbit for awhile, fall into the L2, exit the Jupiter Realm at L1 and then orbit in the sun realm for awhile, and then fall back into the Jupiter realm at L1.I've witnessed similar behavior in the earth moon system. I've seen pellets thrown out of the system in what looks to my eyes like hyperbolic orbits. Whether the V infinity is sufficient for Mars Hohmann injection, I don't know.Although I've seen pellets with near earth perigees, I haven't seen any that evolve into low circular orbits -- the high point apogees seem to remain fairly distant from the earth. What this tells me is that parking in low, circular earth orbits may require delta V to enter and exit.Quote from: sdsds on 08/24/2009 07:10 pmDoes this region include Mars and the asteroids? Is this a strictly 2-D sim, and how careful need we be extrapolating results to 3-D?I don't know how practical these orbits are for reaching Mars or the asteroids. I can tell you there are relatively low delta V paths between EML1 and LEO or between EML1 and Mars using plain old patched conic paths.Whether you can reach Mars using virtually no delta V is something I still don't know.The Sun-asteroid Lagrange points would be so close to the asteroids that they'd useless, I think. Quote from: sdsds on 08/24/2009 07:10 pmOn a topic related to L1 but not low-delta-v trajectories: is it fair to characterize EML1 as a "launch site neutral" destination, i.e. is the delta-v to reach EML1 from any terrestrial launch site the same?Plane changes at a high apogee take less delta-V. It seems to me it'd take a little less delta V to send a payload earthward in the moon's orbital plane. But it wouldn't be very expensive to send payloads earthward in other inclinations, I believe.