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symplectic
This term is a highly specialized technical adjective used almost exclusively in the domains of differential geometry, theoretical physics, and classical mechanics. It describes a specific geometric structure that allows for the definition of Hamiltonian dynamics, where the preservation of the symplectic form corresponds to the conservation of phase space volume (Liouville's theorem).
Because it is a term of art in mathematics, it does not have a general-purpose or metaphorical application in common English. It is typically paired with nouns like manifold, form, capacity, or integrator to specify the mathematical object being discussed.
Meanings
Examples
The phase space of a classical system is naturally a symplectic manifold.
Do we need to assume the manifold is symplectic for this proof to hold?
I wonder if there is a symplectic map that preserves this specific volume.
The researcher focused on the symplectic structure of the cotangent bundle.
We must use a symplectic integrator to maintain the energy conservation of the orbit.
This theorem describes the properties of a closed symplectic form.
Is the transformation symplectic or just a general diffeomorphism?
Is the transformation symplectic or just a general diffeomorphism?
The geometry of the system is fundamentally symplectic in nature.