The corresponding Runge–Lenz vector is more complicated, A = 1 m r 2 ω ω 0 A − − m r 2 E + L 2 { ( p × × L ) + ( m r ω ω 0 A − − m r E ) r ^ ^ } , where ω ω 0 = k m is the natural oscillation frequency, and A = ( E 2 − − ω ω 2 L 2 ) 1 / 2 / ω ω .