Symplectic geometry & classical mechanics, Lecture 10

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry.

Here in the 10th lecture, I introduce flows of vector fields and the Lie derivative.

[김간디]

I have been curious about why we must have several ways of comparing tangent vectors at different points. Now I learned that threre are geometries in which there is no canonical parallel tranportation. Sympletic geometry is one of them! So if we are to compare tangent vectors, we need Lie derivative! If I didn't try to study sympletic geometry, and watch your videos, then I wouldn't have realize that! Thank you so much!

[SkanderTALEBHACINE]

Thanks alot dear Pr, could you please give me some titles (books, articles, websites, ....)about prerequisit. on very basic differential geometry. thanks again also for the your valuable efforts

[reinerwilhelms-tricarico]

Regarding isotopy: In the example of knots and the deformations of them, are we talking of a flow in the length direction of the string or rope ? Or is this folding or unfolding of knots a flow in the embedding space, e.g. R^3 ?