1:55 to the reader... be aware the "N" and the "i" in the coordinates refer to "one particle and one direction" so this could be "x and Vx" or it could be "y and Vy" etc as a couple examples. If one particle was tracked by x , y and z then there would be a 6 dimension phase space and 3 degrees of freedom. If it was two particles , then 12 dimension phase space and 6 degrees of freedom. Some textbooks use N as the number of particles and n in place of the N and i used in this video.
so for a non-chaotic systems, if we have a circular area of a phase space bundle in the beginning, the shape will more-or-less stay the same over time? (the area itself will due to liouville's theorem)
1:55 to the reader... be aware the "N" and the "i" in the coordinates refer to "one particle and one direction" so this could be "x and Vx" or it could be "y and Vy" etc as a couple examples. If one particle was tracked by x , y and z then there would be a 6 dimension phase space and 3 degrees of freedom. If it was two particles , then 12 dimension phase space and 6 degrees of freedom. Some textbooks use N as the number of particles and n in place of the N and i used in this video.
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Sir..ur awesome...tank u for providing for free education
so for a non-chaotic systems, if we have a circular area of a phase space bundle in the beginning, the shape will more-or-less stay the same over time? (the area itself will due to liouville's theorem)
Is it possible to envolve disipative forces in langrange and hamilton method of solving problems
Thank you for this very helpful video sir!
Next level..
Beautiful