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It is sometimes claimed that classical mechanics motivates introduction of symplectic manifolds. This is due to the theorem that the Hamiltonian flow preserves the symplectic form on the phase space.

I am wondering whether symplectic geometry has applications to classical mechanics. Was this connection useful for classical mechanics? Were methods of symplectic geometry relevant for it via, say, the above theorem?

It is sometimes claimed that classical mechanics motivates introduction of symplectic manifolds. This is due to the theorem that the Hamiltonian flow preserves the symplectic form on the phase space.

I am wondering whether symplectic geometry has applications to classical mechanics. Was this connection useful for classical mechanics? Were methods of symplectic geometry relevant for it via, say, the above theorem?

It is claimed that classical mechanics motivates introduction of symplectic manifolds. This is due to the theorem that the Hamiltonian flow preserves the symplectic form on the phase space.

I am wondering whether symplectic geometry has applications to classical mechanics. Was this connection useful for classical mechanics? Were methods of symplectic geometry relevant for it via, say, the above theorem?

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asv
asv
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  • 54
  • 121

Applications of symplectic geometry to classical mechanics

It is sometimes claimed that classical mechanics motivates introduction of symplectic manifolds. This is due to the theorem that the Hamiltonian flow preserves the symplectic form on the phase space.

I am wondering whether symplectic geometry has applications to classical mechanics. Was this connection useful for classical mechanics? Were methods of symplectic geometry relevant for it via, say, the above theorem?