Lie bracket visualized: how second-order residue lets wheeled robots move without sliding
burny_tech · x · 2026-11-12
@mathemetica shares a clean visual explainer of the Lie bracket: flowing X(δt), Y(δt), −X(δt), −Y(δt) doesn't close the loop — the residual [X, Y] δt² measures the failure of X and Y to commute, via [X, Y] = dY·X − dX·Y. When [X, Y] ∉ Lin(X, Y), the distribution is non-integrable and the constraint is nonholonomic: the missing direction appears only at second order. That residual is exactly what allows wheeled systems to maneuver without free sliding.
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