Application of Manifold Theory to Hamiltonian Mechanics
نویسنده
چکیده
In elementary physics, in order to describe the motion of a physical system, a few quantities need to be specified. In 1833, Irish mathematician Hamilton proposed a new formalism of physics. Given a physical system, two sets of first order differential equations can capture all the information. With the aid of the mathematical concept of manifolds, which was developed later, Hamiltonian formalism can describe the objects whose motion is not constrained to Euclidean spaces. Hence, it became a pillar of modern physics. This paper aims to introduce the reader to the Hamiltonian formalism of physics using the theory of manifolds.
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