# Noncommutative version of an arbitrary nondegenerated mechanics

@article{Deriglazov2002NoncommutativeVO, title={Noncommutative version of an arbitrary nondegenerated mechanics}, author={Alexei A. Deriglazov}, journal={arXiv: High Energy Physics - Theory}, year={2002} }

A procedure to obtain noncommutative version for any nondegenerated dynamical system is proposed and discussed. The procedure is as follow. Let $S=\int dt L(q^A, ~ \dot q^A)$ is action of some nondegenerated system, and $L_1(q^A, ~ \dot q^A, ~ v_A)$ is the corresponding first order Lagrangian. Then the corresponding noncommutative version is $S_N=\int dt[ L_1(q^A, ~ \dot q^A, \~ v_A)+ \dot v_A\theta^{AB}v_B]$. Namely, the system $S_N$ has the following properties: 1) It has the same number of…

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