In differential geometry and differential opology, areas of mathematics, a symphonic variety is a smooth variety, M, which is equipped with a closed undisturbed differential 2-form, ω, which is called the symbolic form. The study of symplectic varieties is called symplectic geometry or symplectic topology. Symptomatic varieties arise naturally in abstract formulations of classical mechanics and analytical mechanics as the coraak bundles of varieties, such as in Hamilton formalism of classical mechanics, which provides one of the main motivations for this field of study: The collection of all possible configurations of A system is modeled as a variety, and this variety of hair coraak bundle describes the system's phase space.
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