Worked example - angular momentum conservation from brackets. H = p^2/2m + V(r) with V depending only on r = |q| (central potential). L_z = x p_y - y p_x. Compute [L_z, H]: the kinetic part [L_z, p^2/2m] = 0 by rotational symmetry of p^2 (check: [x p_y, p_x^2] terms cancel pairwise). The potential part: [L_z, V(r)] = dV/dr [L_z, r]; and [L_z, r] = 0 since r is rotationally invariant (x^2+y^2+z^2 unchanged by z-rotation: [x p_y - y p_x, x^2+y^2] = 0 by direct computation). Hence [L_z, H] = 0, so dL_z/dt = 0: angular momentum about z is conserved. Noether's theorem in bracket language - symmetry under rotation gives conservation, verified in a few lines.