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An example of a
While the above example gives a two-dimensional "summary" of a
three-dimensional process, in general, a The orbit example above actually is flawed: an orbit might intersect a plane at a point, and later intersect it at the same point yet moving in some other direction, so, by definition, a function wouldn't be able to take the role of its associated Poincaré Map. Thus, a Poincaré section to analyze an orbit might more likely be done on a 6-dimensional space that also includes three dimensions of velocity (or momentum), reducing it to 5-dimensional summary. mathematics,dynamics)http://dspace.mit.edu/bitstream/handle/1721.1/84612/12-006j-fall-2006/contents/lecture-notes/lecnotes8.pdf |