Abstract
The least action principle is the basic principle of the Newtonian mechanics and geometrical optics. Various forms of analytical mechanics are based on the principle of least action., including Lagrange mechanics, Hamiltonian mechanics and Hertz mechanics based on the principle of minimum curvature. Max Planck believed that this principle is not limited to a particular coordinate system, it can directly applied on the dynamics and the thermodynamics process without losing its universality. Quantum mechanics starts from action quantization, and its various forms include the mathematical structure of analytical mechanics.Quantum mechanics offers a combination of Newtonian and Einsteinian features. Schrodinger believed that quantum wave function has curvature characteristics.

Keywords
The principle of least action, The principle of least curvature, Non-Euclidean line element.

Cite this paper
Wu Xinzhong, Analytic mechanics structure of quantum mechanics and relativity space-time , SCIREA Journal of Physics. Volume 1, Issue 2, December 2016 | PP. 108-124.

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