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math-ph2022★ 15 cited
From Second-Order Differential Geometry to Stochastic Geometric Mechanics
Qiao Huang, Jean-Claude Zambrini
Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian mechanics, and the Hamilton-Jacobi theory, are founded on geometric structures such as…
math-ph2012
The research program of Stochastic Deformation (with a view toward Geometric Mechanics)
Jean-Claude Zambrini
We give an overview of a program of Stochastic Deformation of Classical Mechanics and the Calculus of Variations, strongly inspired by the quantization method.