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Hamiltonian systems, symplectic flows, classical integrable systems
28
votes
Accepted
Is $\Bbb S^2 \times \Bbb S^4$ symplectic?
No. Note that $H^2(S^2\times S^4,\mathbb R)$ is one dimensional, spanned by $\pi^*\alpha$, where $\pi:S^2\times S^4\to S^2$ is the projection, and $\alpha$ is a volume form on $S^2$. Suppose $\omega$ …
0
votes
Momentum a cotangent vector
$p$ is the differential of L with respect to the second variable ($\dot q$), so it represents a linear functional on the tangent space at $q, \dot q$), given by
$$ (u,v)\to \frac{d}{dt} L(q,\dot q+tv …