Sir, I have a doubt that has given me a headache. Sir, the non-linear dynamics and chaotic systems you talk about, these are higher level physics and maths concepts, right? I am in 11th grade; are we taught these concepts or not, or are we only taught about simple systems with some assumptions so that the system does not become chaotic, like assuming friction is not present or value of g is constant everywhere? Am I correct, sir?
Thank you for the lectures playlist, Professor Ross. I just finished it, and I really enjoyed it. The videos are very well-made, entertaining, and very useful for anyone who wants to be introduced to 3-body dynamics. I find this area of astrodynamics fascinating. Are there any more videos planned to come out in this series?
Thank you, Professor Ross. I've been really enjoying your CZcams lectures and reading your book fascinating. I have a question: In the book, you discuss some topics in the x-y plane. When considering tube connections between planets, should we account for the x-y-z three dimensions due to different orbital inclinations? Or is discussing in the x-y plane sufficient, given the tubes' extension in the z direction?
Thank you for watching and good question. We introduce the dynamics in the x-y plane, but go on to discuss how these results work well in the 3D case of x-y-z (it's Chapter 9 of the book). You can see it discussed in a couple of other videos, czcams.com/video/fV0kUmtQWZU/video.htmlsi=urFn54S5kZijmsNj&t=687 and czcams.com/video/FwHDEB1VS_0/video.htmlsi=zXz4vuHIgsNXP_kZ&t=1238 The key difference is the addition of two dimensions (z and z velocity) we must search for intersections between tubes. Numerically, we can do this, even if it's harder to visualized.
Thank you, Professor Ross, for your helpful response. I appreciate the additional video references. Looking forward to exploring more in Chapter 9 and your other materials@@ProfessorRoss
Thank you. Good question. And YES, the method works in the 6-dimensional phase space as well. You can see it discussed in a couple of other videos, czcams.com/video/fV0kUmtQWZU/video.htmlsi=urFn54S5kZijmsNj&t=687 and czcams.com/video/FwHDEB1VS_0/video.htmlsi=zXz4vuHIgsNXP_kZ&t=1238
Thank you for your videos. My question is, the Monodromy Matrix is the same for every states associated to the same periodic orbit? I tried with the code and it looks like (e.g.) the stable eigenvector is almost the same (maybe slight differences are due to numerical errors?) if i put as input several states, only propagated in time, of the same periodic orbit.
The stable eigenvector along the orbit does change *slightly*, but they are very close to each other, as you've found. I've got a nice illustration of this for a 3D halo orbit in Figure 6.2 of my first paper, here: ross.aoe.vt.edu/papers/hetero_halos_2000_original.pdf
how would the scripts be modified to show an NRHO orbit, when using the halo_manifolds script i change the azlp variable to ~1.2 but cannot get the script to run with a amplitude past .5 without getting errors.
Thank you for that whole set of lectures regarding 3BP!
It's my pleasure
Sir, I have a doubt that has given me a headache. Sir, the non-linear dynamics and chaotic systems you talk about, these are higher level physics and maths concepts, right? I am in 11th grade; are we taught these concepts or not, or are we only taught about simple systems with some assumptions so that the system does not become chaotic, like assuming friction is not present or value of g is constant everywhere? Am I correct, sir?
Thank you for the lectures playlist, Professor Ross. I just finished it, and I really enjoyed it. The videos are very well-made, entertaining, and very useful for anyone who wants to be introduced to 3-body dynamics. I find this area of astrodynamics fascinating. Are there any more videos planned to come out in this series?
Glad you like them! I did plan on making more, when I get around to teaching a class on this.
Thank you, Professor Ross. I've been really enjoying your CZcams lectures and reading your book fascinating. I have a question: In the book, you discuss some topics in the x-y plane. When considering tube connections between planets, should we account for the x-y-z three dimensions due to different orbital inclinations? Or is discussing in the x-y plane sufficient, given the tubes' extension in the z direction?
Thank you for watching and good question. We introduce the dynamics in the x-y plane, but go on to discuss how these results work well in the 3D case of x-y-z (it's Chapter 9 of the book). You can see it discussed in a couple of other videos, czcams.com/video/fV0kUmtQWZU/video.htmlsi=urFn54S5kZijmsNj&t=687 and czcams.com/video/FwHDEB1VS_0/video.htmlsi=zXz4vuHIgsNXP_kZ&t=1238 The key difference is the addition of two dimensions (z and z velocity) we must search for intersections between tubes. Numerically, we can do this, even if it's harder to visualized.
Thank you, Professor Ross, for your helpful response. I appreciate the additional video references. Looking forward to exploring more in Chapter 9 and your other materials@@ProfessorRoss
I really enjoyed this lecture! How does this method scale up to the full 6DOF phase space?
Thank you. Good question. And YES, the method works in the 6-dimensional phase space as well. You can see it discussed in a couple of other videos, czcams.com/video/fV0kUmtQWZU/video.htmlsi=urFn54S5kZijmsNj&t=687 and czcams.com/video/FwHDEB1VS_0/video.htmlsi=zXz4vuHIgsNXP_kZ&t=1238
Thank you for your videos. My question is, the Monodromy Matrix is the same for every states associated to the same periodic orbit? I tried with the code and it looks like (e.g.) the stable eigenvector is almost the same (maybe slight differences are due to numerical errors?) if i put as input several states, only propagated in time, of the same periodic orbit.
The stable eigenvector along the orbit does change *slightly*, but they are very close to each other, as you've found. I've got a nice illustration of this for a 3D halo orbit in Figure 6.2 of my first paper, here: ross.aoe.vt.edu/papers/hetero_halos_2000_original.pdf
how would the scripts be modified to show an NRHO orbit, when using the halo_manifolds script i change the azlp variable to ~1.2 but cannot get the script to run with a amplitude past .5 without getting errors.