A Lagrange-D’Alembert Principle and random ODE

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The discussion centers on the Lagrange-D'Alembert Principle and its generalization to mechanics-like ordinary differential equations (ODE) in Banach spaces. The author invites criticism and comments on their paper, which explores applications such as geodesics in infinite-dimensional manifolds and random ODEs with nonholonomic constraints. Additionally, there is a suggestion to relate the principle to quantum mechanics, particularly regarding the time evolution described by the Schrödinger equation. The author references their previous work to support this exploration. Overall, the conversation emphasizes the intersection of classical mechanics and quantum mechanics through advanced mathematical frameworks.
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Here is my paper. A criticism and other comments are welcome.

Abstract: The Lagrange-D'Alembert Principle is one of the fundamental tools of classical mechanics. We generalize this principle to mechanics-like ODE in Banach spaces.
As an application we discuss geodesics in infinite dimensional manifolds and a random ODE with nonholonomic constraint.

https://arxiv.org/abs/2112.05276v3
 
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Interesting.

In Quantum mechanics, the time evolution given by the Schrodinger equation can be restated as a infinite dimensional (classical) Hamiltonian system (at least for the discrete spectrum case). So I wonder if you could state a Lagrange-D'Alembert principle for QM

I give a review of the above statement in https://arxiv.org/abs/2107.07050
 
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