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Results tagged with sg.symplectic-geometry
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user 2837
Hamiltonian systems, symplectic flows, classical integrable systems
6
votes
2
answers
1k
views
Two versions of hamiltonian reduction
Given a symplectic manifold $X$ with nice $G$ action, equivariant momentmap $\mu$ and
invariant $\chi \in \mathfrak{g}^*$ which is a regular value of $\mu$.
There are two ways to form the Hamiltonia …
- 13.2k
24
votes
3
answers
3k
views
Classical mechanics motivation for poisson manifolds?
Suppose I want to understand classical mechanics.
Why should I be interested in arbitrary poisson manifolds and not just in symplectic ones?
What are examples of systems best described by non sympl …
- 13.2k
78
votes
10
answers
18k
views
What is a Lagrangian submanifold intuitively?
What are good ways to think about Lagrangian submanifolds?
Why should one care about them?
More generally: same questions about (co)isotropic ones.
Answers from a classical mechanics point of view …
- 13.2k
50
votes
4
answers
16k
views
What is a symplectic form intuitively?
Hi,
to completely describe a classical mechanical system, you need to do three things:
-Specify a manifold $X$, the phase space. Intuitively this is the space of all possible states of your system.
…
- 13.2k