\begin{array} { r l } { \dot { x } } & { { } = \varepsilon _ { \mathrm { w } } \, \mathrm { c } _ { } ( z ) \cos \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \left( x - t \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \right) - ( v _ { { \mathrm { s } } \parallel } - v _ { { \mathrm { s } } \bot } ) \cos \phi \sin \phi \sin ^ { 2 } \theta , } \\ { \dot { y } } & { { } = - ( v _ { { \mathrm { s } } \parallel } - v _ { { \mathrm { s } } \bot } ) \cos \phi \cos \theta \sin \theta , } \\ { \dot { z } } & { { } = \varepsilon _ { \mathrm { w } } \, \mathrm { s } _ { } ( z ) \sin \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \left( x - t \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \right) - v _ { { \mathrm { s } } \bot } - ( v _ { { \mathrm { s } } \parallel } - v _ { { \mathrm { s } } \bot } ) \cos ^ { 2 } \phi \sin ^ { 2 } \theta , } \\ { \dot { \phi } } & { { } = \lambda \, \varepsilon _ { \mathrm { w } } \, \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \left[ \mathrm { s } _ { } ( z ) \cos { ( x - t ) } \cos { 2 \phi } - \mathrm { c } _ { } ( z ) \sin { ( x - t ) } \sin { 2 \phi } \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \right] , } \\ { \dot { \theta } } & { { } = \lambda \, \varepsilon _ { \mathrm { w } } \, \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \mathopen { } \mathclose \bgroup \left[ \mathrm { s } _ { } ( z ) \cos { ( x - t ) } \sin { 2 \phi } + \mathrm { c } _ { } ( z ) \sin { ( x - t ) } \cos { 2 \phi } \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \aftergroup \egroup \right] \sin \theta \cos \theta } \end{array}