Symplectic Geometry in 2D – Points, Lines, Circles

Re:Symplectic Geometry in 2D – Points, Lines, Circles by Koshkin on Monday February 21, 2022 @02:41PM (#30419724)

> vector calculus isn't very intuitive either

That's, by the way, why we have the calculus of differential forms which, unlike vectors with all their flavors (free; polar; axial/pseudo), have a clear geometric meaning, and with which many statements about fields acquire an especially simple form. There are many excellent guides; for the motivation, see, for example, https://www.jpier.org/PIER/pier148/09.14063009.pdf

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Re:Symplectic Geometry in 2D – Points, Lines, Circles by onedognight on Tuesday February 22, 2022 @08:36AM (#30427727)

Differential forms are a sub-algebra of the geometric algebra, so you don’t give up any of the beautiful things you mentioned.

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Re:Symplectic Geometry in 2D – Points, Lines, Circles by fango on Tuesday February 22, 2022 @06:36AM (#30426625)

yes ... V.I.Arnold - important symplectic geometry author tells us: "Hamilton mechanics cannot be understood without differential forms ...". Thanks for your link.

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