上游充通大学 SHANGHAI JIAO TONG UNIVERSITY Differentiation of complex polar vectors: Let R=R e represent the position of a point with respect to a fixed reference origin,then First order: 乐Re)-ae+Re+0c Second order: 乐Re-+a0je+(i+je+版e =Re+20e9+iRe°-R0e0 -(R-RO2)e+(20R+0R)i eiDifferentiation of complex polar vectors: jθ R e f θ Let represent the position o R = f a point with respect to a fixed reference origin, then Fi d rst or der: ( ) ( )= d jj j j j R e Re R e j Re R j e θ θθ θ θ =+ + θ θ     ( ) ( )= jj j j j R e Re R e j Re R j e dt =+ + θ θ 2 Second order: ( ) ( )( ) ( ) d jj j j j R R Rj R Rj Rj j θθ θ θ θ + ++ + θ θθ θ θ         2 2 ( ) ( )( ) ( ) = 2 jj j j j j j jj R e R e R j e R Rj e R j e j dt Re Rj e Rj e R e θθ θ θ θ θ θ θθ θ θθ θ θ θθ θ = + ++ + + + −      2 2 =( ) +(2 ) j Re Rj e Rj e R e RR e R R θ θθ θ θ θθ + + − +      j j e θ