Jacobi-Lie bracket

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The Jacobi-Lie bracket is a Lie bracketing operation on vector fields given by

[X,Y] = J(X)Y − J(Y)X

where X and Y are vector fields and J denotes the Jacobian.

[edit] Applications

The Jacobi-Lie bracket is essential to proving small-time local controllability (STLC) for driftless affine control systems.

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