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.