Phase space trajectories
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Күн бұрынClassical Mechanics and Relativity: Lecture 12
Theoretical physicist Dr Andrew Mitchell presents an undergraduate lecture course on Classical Mechanics and Relativity at University College Dublin. This is a complete, self-contained, and standalone course in which everything is derived from scratch.
In this lecture I discuss phase space and the dynamics of classical systems in terms of the trajectory through phase space. We will see that periodic systems have bounded phase space orbits, and that systems follow the phase space contours of constant energy. Chaotic systems are also discussed.
Full lecture course playlist: • Classical Mechanics an...
Course textbooks:
"Classical Mechanics" by Goldstein, Safko, and Poole
"Classical Mechanics" by Morin
"Relativity" by Rindler
@waynelast1685 9 ай бұрын
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.
@AlirezaNowroozi-ir6wk 4 ай бұрын
Thats great prof....you are a real teacher...❤❤❤❤
@unkownuser1042 2 жыл бұрын
Sir..ur awesome...tank u for providing for free education
@GeoffryGifari Жыл бұрын
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)
@shinynoob4890 Жыл бұрын
Thank you for this very helpful video sir!
@unkownuser1042 2 жыл бұрын
Next level..
@mirkodobrota4861 Жыл бұрын
Is it possible to envolve disipative forces in langrange and hamilton method of solving problems
@camac7988 3 жыл бұрын
Beautiful
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