Abstract
We describe the “Lie algebra of classical mechanics,” modelled on the Lie algebra generated by kinetic and potential energy of a simple mechanical system with respect to the canonical Poisson bracket. It is a polynomially graded Lie algebra, a class we introduce. We describe these Lie algebras, give an algorithm to calculate the dimensions cn of the homogeneous subspaces of the Lie algebra of classical mechanics, and determine the value of its entropy limn→∞ cn1/n. It is 1.825 423 774 201 08… , a fundamental constant associated with classical mechanics.
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