Corrections to “The Optimal Lift–Drag Ratio of Underwater Glider for Improving Sailing Efficiency”

In [1], there was an error in the third line of equation (20). The correct equation (20) is as follows: \begin{equation*} \left\{ \begin{array}{l} {x_1} = \sqrt { - \frac{2}{9} + \frac{{16{K_D}{K_{D0}}}}{{9{K_L}^2}} + \frac{{2 \times {2^{2/3}}}}{{9Z}} + \frac{{128 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{9{K_L}^4Z}} + \frac{{40 \times {2^{2/3}}{K_D}{K_{D0}}}}{{9{K_L}^2Z}} + \frac{1}{9} \times {2^{1/3}}Z} \\ {x_2} = - \sqrt { - \frac{2}{9} + \frac{{16{K_D}{K_{D0}}}}{{9{K_L}^2}} + \frac{{2 \times {2^{2/3}}}}{{9Z}} + \frac{{128 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{9{K_L}^4Z}} + \frac{{40 \times {2^{2/3}}{K_D}{K_{D0}}}}{{9{K_L}^2Z}} + \frac{1}{9} \times {2^{1/3}}Z} \\ {x_3} = \sqrt{\begin{array}{l} - \frac{2}{9} + \frac{{16{K_D}{K_{D0}}}}{{9{K_L}^2}} - \frac{{{2^{2/3}}}}{{9Z}} + \frac{{{2^{2/3}}}}{{3\sqrt 3 Z}}{\rm{i}} - \frac{{64 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{9{K_L}^4Z}} + \frac{{64 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{3\sqrt 3 {K_L}^4Z}}{\rm{i}} \\ -\frac{{20 \times {2^{2/3}}{K_D}{K_{D0}}}}{{9{K_L}^2Z}} + \frac{{20 \times {2^{2/3}}{K_D}{K_{D0}}}}{{3\sqrt 3 {K_L}^2Z}}{\rm{i}} - \frac{Z}{{9 \times {2^{2/3}}}} - \frac{Z}{{3 \times {2^{2/3}}\sqrt 3}}{\rm{i}} \end{array}}\\ {x_4} = - \sqrt {\begin{array}{l} - \frac{2}{9} + \frac{{16{K_D}{K_{D0}}}}{{9{K_L}^2}} - \frac{{{2^{2/3}}}}{{9Z}} + \frac{{{2^{2/3}}}}{{3\sqrt 3 Z}}{\rm{i}} - \frac{{64 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{9{K_L}^4Z}} + \frac{{64 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{3\sqrt 3 {K_L}^4Z}}{\rm{i}} \\ -\frac{{20 \times {2^{2/3}}{K_D}{K_{D0}}}}{{9{K_L}^2Z}} + \frac{{20 \times {2^{2/3}}{K_D}{K_{D0}}}}{{3\sqrt 3 {K_L}^2Z}}{\rm{i}} - \frac{Z}{{9 \times {2^{2/3}}}} - \frac{Z}{{3 \times {2^{2/3}}\sqrt 3}}{\rm{i}} \end{array}} \\ {x_5} = \sqrt {\begin{array}{l} - \frac{2}{9} + \frac{{16{K_D}{K_{D0}}}}{{9{K_L}^2}} - \frac{{{2^{2/3}}}}{{9Z}} - \frac{{{2^{2/3}}}}{{3\sqrt 3 Z}}{\rm{i}} - \frac{{64 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{9{K_L}^4Z}} - \frac{{64 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{3\sqrt 3 {K_L}^4Z}}{\rm{i}} - \\ \frac{{20 \times {2^{2/3}}{K_D}{K_{D0}}}}{{9{K_L}^2Z}} - \frac{{20 \times {2^{2/3}}{K_D}{K_{D0}}}}{{3\sqrt 3 {K_L}^2Z}}{\rm{i}} - \frac{Z}{{9 \times {2^{2/3}}}} + \frac{Z}{{3 \times {2^{2/3}}\sqrt 3}}{\rm{i}} \end{array}} \\ {x_6} = - \sqrt {\begin{array}{l} - \frac{2}{9} + \frac{{16{K_D}{K_{D0}}}}{{9{K_L}^2}} - \frac{{{2^{2/3}}}}{{9Z}} - \frac{{{2^{2/3}}}}{{3\sqrt 3 Z}}{\rm{i}} - \frac{{64 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{9{K_L}^4Z}} - \frac{{64 \times {2^{2/3}}{K_D}^2{K_{D0}}^2}}{{3\sqrt 3 {K_L}^4Z}}{\rm{i}} \\ -\frac{{20 \times {2^{2/3}}{K_D}{K_{D0}}}}{{9{K_L}^2Z}} - \frac{{20 \times {2^{2/3}}{K_D}{K_{D0}}}}{{3\sqrt 3 {K_L}^2Z}}{\rm{i}} - \frac{Z}{{9 \times {2^{2/3}}}} + \frac{Z}{{3 \times {2^{2/3}}\sqrt 3}}{\rm{i}} \end{array}} \\ {x_7} = {\rm{i}}\\ {x_8} = - {\rm{i}} \end{array} \right. \end{equation*}