APPENDIX A1
$${{a}_{{11}}} = 1,\quad {{a}_{{12}}} = \left[ {\lambda {\kern 1pt} '\, + (2\mu {\kern 1pt} '\, + K{\kern 1pt} ')(1 - s_{{21}}^{2}{{{\sin }}^{2}}{{\theta }_{0}}) + \frac{{\beta _{0}^{'}{{\zeta }_{2}}}}{{l_{2}^{2}}}} \right]{\text{/}}{{D}_{1}}s_{{21}}^{2},$$
$${{a}_{{1s}}} = (2\mu {\kern 1pt} '\, + K{\kern 1pt} ')\sin {{\theta }_{0}}\sqrt {(1 - s_{{s1}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{1}}{{s}_{{s1}}},$$
$${{a}_{{1t}}} = - [\lambda ''\, + (2\mu ''\, + K'')(1 - S_{{t1}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) + \beta _{0}^{{''}}\zeta _{t}^{'}]{\text{/}}{{D}_{1}}S_{{t1}}^{{'2}},$$
$${{a}_{{1q}}} = (2\mu {\kern 1pt} ''\, + K{\kern 1pt} '')\sin {{\theta }_{0}}\sqrt {(1 - S_{{q1}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{1}}S_{{q1}}^{'},$$
$${{a}_{{21}}} = \sin {{\theta }_{0}}\cos {{\theta }_{0}},\quad {{a}_{{22}}} = \sin {{\theta }_{0}}\sqrt {(1 - s_{{21}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{21}}},$$
$${{a}_{{2s}}} = - \left[ {\mu {\kern 1pt} '(1 - 2s_{{s1}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) + K{\kern 1pt} '(1 - s_{{s1}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) - \frac{{K'{{\eta }_{s}}}}{{l_{s}^{2}}}} \right]{\text{/}}{{D}_{2}}s_{{s1}}^{2},$$
$${{a}_{{2t}}} = (2\mu {\kern 1pt} ''\, + K{\kern 1pt} '')\sin {{\theta }_{0}}\sqrt {(1 - S_{{t1}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{2}}S_{{t1}}^{'},$$
$${{a}_{{2q}}} = [\mu {\kern 1pt} ''(1 - 2S_{{q1}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) + K{\kern 1pt} ''(1 - S_{{q1}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) - K{\kern 1pt} ''\eta _{q}^{'}]{\text{/}}{{D}_{2}}S_{{q1}}^{{'2}},$$
$${{a}_{{33}}} = \sqrt {1 - s_{{31}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}{{s}_{{31}}},\quad {{a}_{{34}}} = {{\eta }_{4}}\sqrt {1 - s_{{41}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}{{\eta }_{3}}{{s}_{{41}}},$$
$${{a}_{{37}}} = \gamma {\kern 1pt} '\eta _{3}^{'}\sqrt {1 - s_{{31}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}s_{{31}}^{'}\gamma {\kern 1pt} '{{\eta }_{3}},\quad {{a}_{{38}}} = \gamma ''\eta _{4}^{'}\sqrt {1 - s_{{41}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}s_{{41}}^{'}\gamma {\kern 1pt} '{{\eta }_{3}},$$
$${{a}_{{41}}} = \cos {{\theta }_{0}},\quad {{a}_{{42}}} = {{\zeta }_{2}}\sqrt {(1 - s_{{21}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{\zeta }_{1}}{{s}_{{21}}},$$
$${{a}_{{45}}} = Y{\kern 1pt} '\zeta _{1}^{'}\sqrt {1 - s_{{11}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}Y{\kern 1pt} '{{\zeta }_{1}}s_{{11}}^{'},\quad {{a}_{{46}}} = Y''\zeta _{2}^{'}\sqrt {1 - s_{{21}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}Y{\kern 1pt} '{{\zeta }_{1}}s_{{21}}^{'},$$
$${{a}_{{51}}} = \sin {{\theta }_{0}} = {{a}_{{52}}},\quad {{a}_{{5s}}} = - \sqrt {(1 - s_{{s1}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{s1}}},\quad {{a}_{{55}}} = - \sin {{\theta }_{0}} = {{a}_{{56}}},$$
$${{a}_{{5q}}} = - \sqrt {(1 - S_{{q1}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}S_{{q1}}^{'},\quad {{a}_{{61}}} = \cos {{\theta }_{0}},\quad {{a}_{{62}}} = \sqrt {(1 - s_{{21}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{21}}},$$
$${{a}_{{63}}} = \sin {{\theta }_{0}} = {{a}_{{64}}},\quad {{a}_{{6t}}} = \sqrt {(1 - S_{{t1}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}S_{{t1}}^{'},\quad {{a}_{{67}}} = - \sin {{\theta }_{0}} = {{a}_{{68}}},\quad {{a}_{{73}}} = 1,$$
$${{a}_{{74}}} = {{\eta }_{4}}{\text{/}}{{\eta }_{3}},\quad {{a}_{{77}}} = - \eta _{3}^{'}{\text{/}}{{\eta }_{3}},\quad {{a}_{{78}}} = - \eta _{4}^{'}{\text{/}}{{\eta }_{3}},\quad {{a}_{{81}}} = 1,\quad {{a}_{{82}}} = {{\zeta }_{2}}{\text{/}}{{\zeta }_{1}},$$
$${{a}_{{85}}} = - \zeta _{1}^{'}{\text{/}}{{\zeta }_{1}},\quad {{a}_{{86}}} = - \zeta _{2}^{'}{\text{/}}{{\zeta }_{1}},$$
$$s = 3,4;\quad t = 5,6;\quad q = 7,8;$$
$${{s}_{{p1}}} = \frac{{{{S}_{p}}}}{{{{S}_{1}}}},(p = 2,3,4),\quad s_{{r1}}^{'} = \frac{{S_{r}^{'}}}{{{{S}_{1}}}},\quad (r = 1,2,3,4),$$
$$S_{{51}}^{'} = s_{{11}}^{'},\quad S_{{61}}^{'} = s_{{21}}^{'},\quad S_{{71}}^{'} = s_{{31}}^{'},\quad S_{{81}}^{'} = s_{{41}}^{'},\quad \zeta _{5}^{'} = \frac{{\zeta _{1}^{'}}}{{l_{1}^{{'2}}}},\quad \zeta _{6}^{'} = \frac{{\zeta _{2}^{'}}}{{l_{2}^{{'2}}}},\quad \eta _{7}^{'} = \frac{{\eta _{3}^{'}}}{{l_{3}^{{'2}}}},\quad \eta _{5}^{'} = \frac{{\eta _{4}^{'}}}{{l_{4}^{{'2}}}},$$
$${{D}_{1}} = \left[ {\lambda {\kern 1pt} '\, + (2\mu {\kern 1pt} '\, + K{\kern 1pt} '){{{\cos }}^{2}}{{\theta }_{0}} + \frac{{\beta _{0}^{'}{{\zeta }_{1}}}}{{l_{1}^{2}}}} \right],\quad {{D}_{2}} = (2\mu {\kern 1pt} '\, + K{\kern 1pt} '),\quad {{Y}_{1}} = - 1,\quad {{Y}_{2}} = \sin {{\theta }_{0}}\cos {{\theta }_{0}},$$
$${{Y}_{3}} = 0,\quad {{Y}_{4}} = \cos {{\theta }_{0}},\quad {{Y}_{5}} = - \sin {{\theta }_{0}},\quad {{Y}_{6}} = \cos {{\theta }_{0}},\quad {{Y}_{7}} = 0,\quad {{Y}_{8}} = - 1,$$
$${{E}_{1}} = - Z_{1}^{2},\quad {{E}_{2}} = Z_{2}^{2}{{L}_{1}}\left[ {{{\lambda }_{2}} + {{\mu }_{2}} + \frac{{\beta _{0}^{'}{{\zeta }_{2}}}}{{l_{2}^{2}}} - \frac{{{{K}_{2}}\zeta _{2}^{2}}}{{l_{2}^{2}}}} \right]l_{2}^{3}\cos \theta ,$$
$${{E}_{{3,4}}} = Z_{{3,4}}^{2}{{L}_{1}}\left[ {{{\mu }_{2}} + {{K}_{2}} - \frac{{{{\eta }_{{3,4}}}}}{{l_{{3,4}}^{2}}}\left( {{{\gamma }_{2}}{{\eta }_{{3,4}}} + {{K}_{2}}} \right)} \right]l_{{3,4}}^{3}\cos {{\theta }_{{3,4}}},$$
$${{E}_{{5,6}}} = Z_{{5,6}}^{2}{{L}_{1}}\left[ {\lambda _{2}^{'} + \mu _{2}^{'} + \frac{{\beta _{0}^{{''}}\zeta _{2}^{'}}}{{l_{2}^{{'2}}}} - \frac{{K_{2}^{'}\zeta _{2}^{{'2}}}}{{l_{2}^{{'2}}}}} \right]l_{{1,2}}^{{'3}}\cos \theta _{{1,2}}^{'},$$
$${{E}_{{7,8}}} = Z_{{7,8}}^{2}{{L}_{1}}\left[ {(\mu _{2}^{'} + K_{2}^{'} - \frac{{{{\eta }_{{3,4}}}}}{{l_{{3,4}}^{{'2}}}}(\gamma _{2}^{'}\eta _{{3,4}}^{'} + K_{2}^{'})} \right]l_{{3,4}}^{{'3}}\cos \theta _{{3,4}}^{'},\quad {{L}_{1}} = {{\left[ {{{\lambda }_{2}} + {{\mu }_{2}} + \frac{{\beta _{0}^{'}{{\zeta }_{2}}}}{{l_{1}^{2}}} - \frac{{{{K}_{2}}\zeta _{1}^{2}}}{{l_{1}^{2}}}} \right]}^{{ - 1}}},$$
APPENDIX A2
$${{a}_{{11}}} = \left[ {\lambda {\kern 1pt} '\, + (2\mu {\kern 1pt} '\, + K{\kern 1pt} ')(1 - s_{{12}}^{2}{{{\sin }}^{2}}{{\theta }_{0}}) + \frac{{\beta _{0}^{'}{{\zeta }_{1}}}}{{l_{2}^{2}}}} \right]{\text{/}}{{D}_{3}}s_{{12}}^{2},\quad {{a}_{{12}}} = 1,$$
$${{a}_{{1s}}} = (2\mu {\kern 1pt} '\, + K{\kern 1pt} ')\sin {{\theta }_{0}}\sqrt {(1 - s_{{s2}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{3}}{{s}_{{s2}}},$$
$${{a}_{{1t}}} = - [\lambda ''\, + (2\mu ''\, + K'')(1 - S_{{t2}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) + \beta _{0}^{{''}}\zeta _{t}^{'}]{\text{/}}{{D}_{3}}S_{{t2}}^{{'2}},$$
$${{a}_{{1q}}} = (2\mu {\kern 1pt} ''\, + K{\kern 1pt} '')\sin {{\theta }_{0}}\sqrt {(1 - S_{{q2}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{3}}S_{{q2}}^{'},$$
$${{a}_{{21}}} = \sin {{\theta }_{0}}\sqrt {(1 - s_{{12}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{12}}},\quad {{a}_{{22}}} = \sin {{\theta }_{0}}\cos {{\theta }_{0}},$$
$${{a}_{{2s}}} = - \left[ {\mu {\kern 1pt} '(1 - 2s_{{s2}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) + K{\kern 1pt} '(1 - s_{{s2}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) - \frac{{K{\kern 1pt} '{{\eta }_{s}}}}{{l_{s}^{2}}}} \right]{\text{/}}{{D}_{2}}s_{{s2}}^{2},$$
$${{a}_{{2t}}} = (2\mu {\kern 1pt} ''\, + K{\kern 1pt} '')\sin {{\theta }_{0}}\sqrt {(1 - S_{{t2}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{2}}S_{{t2}}^{'},$$
$${{a}_{{2q}}} = [\mu {\kern 1pt} ''(1 - 2S_{{q2}}^{{'2}}{{\sin }^{2}}{{\theta }_{0}}) + K{\kern 1pt} ''(1 - S_{{q2}}^{{'2}}{{\sin }^{2}}{{\theta }_{0}}) - K{\kern 1pt} ''{\kern 1pt} \eta _{q}^{'}]{\text{/}}{{D}_{2}}S_{{q2}}^{{'2}},$$
$${{a}_{{33}}} = \sqrt {1 - s_{{32}}^{2}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}{{s}_{{32}}},\quad {{a}_{{34}}} = {{\eta }_{4}}\sqrt {1 - s_{{42}}^{2}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}{{\eta }_{3}}{{s}_{{42}}},$$
$${{a}_{{37}}} = \gamma ''\eta _{3}^{'}\sqrt {1 - s_{{32}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}s_{{32}}^{'}\gamma {\kern 1pt} '{{\eta }_{3}},\quad {{a}_{{38}}} = \gamma {\kern 1pt} ''\eta _{4}^{'}\sqrt {1 - s_{{42}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}s_{{42}}^{'}\gamma {\kern 1pt} '{{\eta }_{3}},$$
$${{a}_{{41}}} = {{\zeta }_{1}}\sqrt {(1 - s_{{12}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{\zeta }_{2}}{{s}_{{12}}},\quad {{a}_{{42}}} = \cos {{\theta }_{0}},$$
$${{a}_{{45}}} = Y{\kern 1pt} ''\zeta _{1}^{'}\sqrt {1 - s_{{12}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}Y{\kern 1pt} '{{\zeta }_{2}}s_{{12}}^{'},\quad {{a}_{{46}}} = Y{\kern 1pt} ''\zeta _{2}^{'}\sqrt {1 - s_{{22}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}Y{\kern 1pt} '{{\zeta }_{2}}s_{{22}}^{'},$$
$${{a}_{{51}}} = {\text{sin}}{{\theta }_{0}} = {{a}_{{52}}},\quad {{a}_{{5s}}} = - \sqrt {(1 - s_{{s2}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{s2}}},\quad {{a}_{{55}}} = - \sin {{\theta }_{0}} = {{a}_{{56}}},$$
$${{a}_{{5q}}} = - \sqrt {(1 - S_{{q2}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}S_{{q2}}^{'},\quad {{a}_{{61}}} = \sqrt {(1 - s_{{12}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{12}}},\quad {{a}_{{62}}} = \cos {{\theta }_{0}},$$
$${{a}_{{63}}} = \sin {{\theta }_{0}} = {{a}_{{64}}},\quad {{a}_{{6t}}} = \sqrt {(1 - S_{{t2}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}S_{{t2}}^{'},\quad {{a}_{{67}}} = - {\text{sin}}{{\theta }_{0}} = {{a}_{{68}}},\quad {{a}_{{73}}} = 1,$$
$${{a}_{{74}}} = {{\eta }_{4}}{\text{/}}{{\eta }_{3}},\quad {{a}_{{77}}} = - \eta _{3}^{'}{\text{/}}{{\eta }_{3}},\quad {{a}_{{78}}} = - \eta _{4}^{'}{\text{/}}{{\eta }_{3}},\quad {{a}_{{81}}} = {{\zeta }_{{\text{1}}}}{\text{/}}{{\zeta }_{2}},$$
$${{a}_{{82}}} = 1,\quad {{a}_{{85}}} = - \zeta _{1}^{'}{\text{/}}{{\zeta }_{2}},\quad {{a}_{{86}}} = - \zeta _{2}^{'}{\text{/}}{{\zeta }_{2}},$$
$${{s}_{{p2}}} = \frac{{{{S}_{p}}}}{{{{S}_{2}}}},(p = 1,3,4),\quad s_{{r2}}^{'} = \frac{{S_{r}^{'}}}{{{{S}_{2}}}},(r = 1,2,3,4),\quad S_{{52}}^{'} = s_{{12}}^{'},\quad S_{{62}}^{'} = s_{{22}}^{'},,$$
$$S_{{72}}^{'} = s_{{32}}^{'},\quad S_{{82}}^{'} = s_{{42}}^{'},\quad {{D}_{3}} = \left[ {\lambda {\kern 1pt} '\, + (2\mu {\kern 1pt} '\, + K{\kern 1pt} '){\text{co}}{{{\text{s}}}^{2}}{{\theta }_{0}} + \frac{{\beta _{0}^{'}{{\zeta }_{2}}}}{{l_{2}^{2}}}} \right],$$
$${{E}_{1}} = Z_{1}^{2}{{L}_{2}}\left[ {{{\lambda }_{2}} + {{\mu }_{2}} + \frac{{\beta _{0}^{'}{{\zeta }_{1}}}}{{l_{1}^{2}}} - \frac{{{{K}_{2}}\zeta _{1}^{2}}}{{l_{1}^{2}}}} \right]l_{1}^{3}{\text{cos}}\theta ,\quad {{E}_{2}} = - Z_{2}^{2},$$
$${{E}_{{3,4}}} = Z_{{3,4}}^{2}{{L}_{2}}\left[ {{{\mu }_{2}} + {{K}_{2}} - \frac{{{{\eta }_{{3,4}}}}}{{l_{{3,4}}^{2}}}\left( {{{\gamma }_{2}}{{\eta }_{{3,4}}} + {{K}_{2}}} \right)} \right]l_{{3,4}}^{3}\cos {{\theta }_{{3,4}}},$$
$${{E}_{{5,6}}} = Z_{{5,6}}^{2}{{L}_{2}}\left[ {\lambda _{2}^{'} + \mu _{2}^{'} + \frac{{\beta _{0}^{{''}}\zeta _{2}^{'}}}{{l_{2}^{{'2}}}} - \frac{{K_{2}^{'}\zeta _{2}^{{'2}}}}{{l_{2}^{{'2}}}}} \right]l_{{1,2}}^{{'3}}\cos \theta _{{1,2}}^{'},$$
$${{E}_{{7,8}}} = Z_{{7,8}}^{2}{{L}_{2}}\left[ {(\mu _{2}^{'} + K_{2}^{'} - \frac{{{{\eta }_{{3,4}}}}}{{l_{{3,4}}^{{'2}}}}(\gamma _{2}^{'}\eta _{{3,4}}^{'} + K_{2}^{'})} \right]l_{{3,4}}^{{'3}}{\text{cos}}\theta _{{3,4}}^{'},\quad {{L}_{2}} = {{\left[ {{{\lambda }_{2}} + {{\mu }_{2}} + \frac{{\beta _{0}^{'}{{\zeta }_{2}}}}{{l_{2}^{2}}} - \frac{{{{K}_{2}}\zeta _{2}^{2}}}{{l_{2}^{2}}}} \right]}^{{ - 1}}}.$$
APPENDIX B1
$${{h}_{{1s}}} = \left[ {\lambda {\kern 1pt} '\, + (2\mu {\kern 1pt} '\, + K{\kern 1pt} ')(1 - s_{{s3}}^{2}{{{\sin }}^{2}}{{\theta }_{0}}) + \frac{{\beta _{0}^{'}{{\zeta }_{s}}}}{{l_{s}^{2}}}} \right]{\text{/}}{{D}_{2}}s_{{s3}}^{2},$$
$${{h}_{{13}}} = \sin {{\theta }_{0}}\cos {{\theta }_{0}},\quad {{h}_{{14}}} = \sin {{\theta }_{0}}\sqrt {(1 - s_{{43}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{43}}},$$
$${{h}_{{1t}}} = - [\lambda {\kern 1pt} ''\, + (2\mu {\kern 1pt} ''\, + K{\kern 1pt} '')(1 - S_{{t3}}^{{'2}}{{\sin }^{2}}{{\theta }_{0}}) + \beta _{0}^{{''}}\zeta _{t}^{'}]{\text{/}}{{D}_{2}}S_{{t3}}^{{'2}},$$
$${{h}_{{1q}}} = (2\mu {\kern 1pt} ''\, + K{\kern 1pt} '')\sin {{\theta }_{0}}\sqrt {(1 - S_{{q3}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{2}}S_{{q3}}^{'},$$
$${{h}_{{2s}}} = (2\mu {\kern 1pt} '\, + K{\kern 1pt} ')\sin {{\theta }_{0}}\sqrt {(1 - s_{{s3}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{4}}{{s}_{{s3}}},\quad {{h}_{{23}}} = - 1,$$
$${{h}_{{24}}} = - \left[ {\mu {\kern 1pt} '(1 - 2s_{{43}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) + K{\kern 1pt} '(1 - s_{{43}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) - \frac{{K{\kern 1pt} '{{\eta }_{4}}}}{{l_{4}^{2}}}} \right]{\text{/}}{{D}_{4}}s_{{43}}^{2},$$
$${{h}_{{2t}}} = (2\mu ''\, + K'')\sin {{\theta }_{0}}\sqrt {(1 - S_{{t3}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{4}}S_{{t3}}^{'},$$
$${{h}_{{2q}}} = [\mu {\kern 1pt} ''(1 - 2S_{{q3}}^{{'2}}{{\sin }^{2}}{{\theta }_{0}}) + K{\kern 1pt} ''(1 - S_{{q3}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) - K{\kern 1pt} ''\eta _{q}^{'}]{\text{/}}{{D}_{4}}S_{{q3}}^{{'2}},$$
$${{h}_{{33}}} = \cos {{\theta }_{0}},\quad {{h}_{{34}}} = {{\eta }_{4}}\sqrt {1 - s_{{43}}^{2}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}{{\eta }_{3}}{{s}_{{43}}},$$
$${{h}_{{37}}} = \gamma {\kern 1pt} ''{\kern 1pt} \eta _{3}^{'}\sqrt {1 - s_{{33}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}s_{{33}}^{'}\gamma {\kern 1pt} '{{\eta }_{3}},\quad {{h}_{{38}}} = \gamma {\kern 1pt} ''{\kern 1pt} \eta _{4}^{'}\sqrt {1 - s_{{43}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}s_{{43}}^{'}\gamma {\kern 1pt} '{{\eta }_{3}},$$
$${{h}_{{4s}}} = \sqrt {(1 - s_{{s3}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{s3}}},\quad {{h}_{{45}}} = Y{\kern 1pt} ''{\kern 1pt} \zeta _{1}^{'}\sqrt {1 - s_{{13}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}Y{\kern 1pt} '{{\zeta }_{1}}s_{{13}}^{'},$$
$${{h}_{{46}}} = Y{\kern 1pt} ''\zeta _{2}^{'}\sqrt {1 - s_{{23}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}Y'{{\zeta }_{1}}s_{{23}}^{'},$$
$${{h}_{{51}}} = \sin {{\theta }_{0}} = {{h}_{{52}}},\quad {{h}_{{53}}} = - \cos {{\theta }_{0}},\quad {{h}_{{54}}} = - \sqrt {(1 - s_{{43}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{43}}},$$
$${{h}_{{55}}} = - \sin {{\theta }_{0}} = {{h}_{{56}}}\quad {{h}_{{5q}}} = - \sqrt {(1 - S_{{q3}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}S_{{q3}}^{'}\quad {{h}_{{6s}}} = - \sqrt {(1 - s_{{s3}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{s3}}},$$
$${{h}_{{63}}} = - \sin {{\theta }_{0}} = {{h}_{{64}}},\quad {{h}_{{6t}}} = - \sqrt {(1 - S_{{t3}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}S_{{t3}}^{'},\quad {{h}_{{67}}} = \sin {{\theta }_{0}} = {{h}_{{68}}},$$
$${{h}_{{73}}} = 1,\quad {{h}_{{74}}} = {{\eta }_{4}}{\text{/}}{{\eta }_{3}},\quad {{h}_{{77}}} = - \eta _{3}^{'}{\text{/}}{{\eta }_{3}},\quad {{h}_{{78}}} = - \eta _{4}^{'}{\text{/}}{{\eta }_{3}},\quad {{h}_{{81}}} = 1,\quad {{h}_{{82}}} = {{\zeta }_{2}}{\text{/}}{{\zeta }_{1}},$$
$${{h}_{{85}}} = - \zeta _{1}^{'}{\text{/}}{{\zeta }_{1}},\quad {{h}_{{86}}} = - \zeta _{2}^{'}{\text{/}}{{\zeta }_{1}},\quad {{W}_{1}} = \sin {{\theta }_{0}}\cos {{\theta }_{0}},\quad {{W}_{2}} = 1,\quad {{W}_{3}} = \cos {{\theta }_{0}},$$
$${{W}_{4}} = 0,\quad {{W}_{5}} = - \cos {{\theta }_{0}},\quad {{W}_{6}} = \sin {{\theta }_{0}},\quad {{W}_{7}} = - 1,\quad {{W}_{8}} = 0,$$
Here now s = 1, 2; \({{s}_{{p3}}} = \frac{{{{S}_{p}}}}{{{{S}_{3}}}},(p = 1,2,4),s_{{r3}}^{'} = \frac{{S_{r}^{'}}}{{{{S}_{3}}}}\), (r = 1, 2, 3, 4) \(S_{{53}}^{'} = s_{{13}}^{'},S_{{63}}^{'} = s_{{23}}^{'}\), \(S_{{73}}^{'} = s_{{33}}^{'}\), \(S_{{83}}^{'} = s_{{43}}^{'}\), \({{D}_{4}} = - \left[ {\mu {\kern 1pt} '{\kern 1pt} \cos 2{{\theta }_{0}} + K{\kern 1pt} '{\kern 1pt} {{{\cos }}^{2}}{{\theta }_{0}} - \frac{{K{\kern 1pt} '{\kern 1pt} {{\eta }_{3}}}}{{l_{3}^{2}}}} \right].\)
$${{E}_{{1,2}}} = Q_{{1,2}}^{2}{{L}_{3}}\left[ {{{\lambda }_{2}} + {{\mu }_{2}} + \frac{{\beta _{0}^{'}{{\zeta }_{{1,2}}}}}{{l_{{1,2}}^{2}}} - \frac{{{{K}_{2}}\zeta _{{1,2}}^{2}}}{{l_{{1,2}}^{2}}}} \right]l_{{1,2}}^{3}{\text{cos}}{{\theta }_{{1,2}}},\quad {{E}_{3}} = - Q_{3}^{2},$$
$${{E}_{4}} = Q_{4}^{2}{{L}_{3}}\left[ {{{\mu }_{2}} + {{K}_{2}} - \frac{{{{\eta }_{4}}}}{{l_{4}^{2}}}\left( {{{\gamma }_{2}}{{\eta }_{4}} + {{K}_{2}}} \right)} \right]l_{4}^{3}\;\cos {{\theta }_{4}},$$
$${{E}_{{5,6}}} = Q_{{5,6}}^{2}{{L}_{3}}\left[ {\lambda _{2}^{'} + \mu _{2}^{'} + \frac{{\beta _{2}^{{''}}\zeta _{2}^{'}}}{{l_{2}^{{'2}}}} - \frac{{K_{2}^{'}\zeta _{2}^{{'2}}}}{{l_{2}^{{'2}}}}} \right]l_{{1,2}}^{{'3}}\cos \theta _{{1,2}}^{'},$$
$${{E}_{{7,8}}} = Q_{{7,8}}^{2}{{L}_{3}}\left[ {(\mu _{2}^{'} + K_{2}^{'} - \frac{{{{\eta }_{{3,4}}}}}{{l_{{3,4}}^{{'2}}}}(\gamma _{2}^{'}\eta _{{3,4}}^{'} + K_{2}^{'})} \right]l_{{3,4}}^{{'3}}\cos \theta _{{3,4}}^{'},\quad {{L}_{3}} = {{\left[ {{{\mu }_{2}} + {{K}_{2}} - \frac{{{{\eta }_{3}}}}{{l_{3}^{2}}}\left( {{{\gamma }_{2}}{{\eta }_{3}} + {{K}_{2}}} \right)} \right]}^{{ - 1}}}.$$
APPENDIX B2
$${{h}_{{1s}}} = \left[ {\lambda {\kern 1pt} '\, + (2\mu {\kern 1pt} '\, + K{\kern 1pt} ')(1 - s_{{s4}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) + \frac{{\beta _{0}^{'}{{\zeta }_{s}}}}{{l_{s}^{2}}}} \right]{\text{/}}{{D}_{2}}s_{{s4}}^{2},$$
$${{h}_{{13}}} = \sin {{\theta }_{0}}\sqrt {(1 - s_{{34}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{34}}},\quad {{h}_{{14}}} = \sin {{\theta }_{0}}\cos {{\theta }_{0}},$$
$${{h}_{{1t}}} = - [\lambda {\kern 1pt} ''\, + (2\mu {\kern 1pt} ''\, + K{\kern 1pt} '')(1 - S_{{t4}}^{{'2}}{{\sin }^{2}}{{\theta }_{0}}) + \beta _{0}^{{''}}\zeta _{t}^{'}]{\text{/}}{{D}_{2}}S_{{t4}}^{{'2}},$$
$${{h}_{{1q}}} = (2\mu ''\, + K'')\sin {{\theta }_{0}}\sqrt {(1 - S_{{q4}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{2}}S_{{q4}}^{'},$$
$${{h}_{{2s}}} = (2\mu {\kern 1pt} '\, + K{\kern 1pt} ')\sin {{\theta }_{0}}\sqrt {(1 - s_{{s4}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{3}}{{s}_{{s4}}},\quad {{h}_{{24}}} = - 1,$$
$${{h}_{{23}}} = - \left[ {\mu '{\kern 1pt} (1 - 2s_{{34}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) + K'{\kern 1pt} (1 - s_{{34}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}) - \frac{{K{\kern 1pt} '{\kern 1pt} {{\eta }_{3}}}}{{l_{3}^{2}}}} \right]{\text{/}}{{D}_{3}}s_{{34}}^{2},$$
$${{h}_{{24}}} = - 1,\quad {{h}_{{2t}}} = (2\mu {\kern 1pt} ''\, + K''){\text{sin}}{{\theta }_{0}}\sqrt {(1 - S_{{t4}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{D}_{3}}S_{{t4}}^{'},$$
$${{h}_{{2q}}} = [\mu {\kern 1pt} ''(1 - 2S_{{q4}}^{{'2}}{{\sin }^{2}}{{\theta }_{0}}) + K{\kern 1pt} ''(1 - S_{{q4}}^{{'2}}{{\sin }^{2}}{{\theta }_{0}}) - K{\kern 1pt} ''\eta _{q}^{'}]{\text{/}}{{D}_{3}}S_{{q4}}^{{'2}},$$
$${{h}_{{33}}} = {{\eta }_{3}}\sqrt {1 - s_{{34}}^{2}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}{{\eta }_{4}}{{s}_{{44}}},\quad {{h}_{{34}}} = \cos {{\theta }_{0}},$$
$${{h}_{{37}}} = \gamma {\kern 1pt} ''\eta _{3}^{'}\sqrt {1 - s_{{34}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}s_{{34}}^{'}\gamma {\kern 1pt} '{{\eta }_{4}},\quad {{h}_{{38}}} = \gamma {\kern 1pt} ''\eta _{4}^{'}\sqrt {1 - s_{{44}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}s_{{44}}^{'}\gamma {\kern 1pt} '{{\eta }_{4}},$$
$${{h}_{{4s}}} = \sqrt {(1 - s_{{s4}}^{2}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{s4}}},\quad {{h}_{{45}}} = Y'{\kern 1pt} '{\kern 1pt} \zeta _{1}^{'}\sqrt {1 - s_{{14}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}}} {\text{/}}Y'{\kern 1pt} {{\zeta }_{1}}s_{{14}}^{'},$$
$${{h}_{{46}}} = Y'{\kern 1pt} '{\kern 1pt} \zeta _{2}^{'}\sqrt {1 - s_{{24}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}}} {\text{/}}Y{\kern 1pt} '{\kern 1pt} {{\zeta }_{1}}s_{{24}}^{'},\quad {{h}_{{51}}} = \sin {{\theta }_{0}} = {{h}_{{52}}},\quad {{h}_{{53}}} = - \sqrt {(1 - s_{{34}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{34}}},$$
$${{h}_{{54}}} = - \cos {{\theta }_{0}},\quad {{h}_{{55}}} = - \sin {{\theta }_{0}} = {{h}_{{56}}},\quad {{h}_{{5q}}} = - \sqrt {(1 - S_{{q4}}^{{'2}}{\text{si}}{{{\text{n}}}^{2}}{{\theta }_{0}})} {\text{/}}S_{{q4}}^{'},$$
$${{h}_{{6s}}} = - \sqrt {(1 - s_{{s4}}^{2}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}{{s}_{{s4}}},\quad {{h}_{{63}}} = - {\text{sin}}{{\theta }_{0}} = {{h}_{{64}}},\quad {{h}_{{6t}}} = - \sqrt {(1 - S_{{t4}}^{{'2}}{{{\sin }}^{2}}{{\theta }_{0}})} {\text{/}}S_{{t4}}^{'},$$
$${{h}_{{67}}} = \sin {{\theta }_{0}} = {{h}_{{68}}},\quad {{h}_{{73}}} = {{\eta }_{3}}{\text{/}}{{\eta }_{4}},\quad {{h}_{{74}}} = 1,\quad {{h}_{{77}}} = - \eta _{3}^{'}{\text{/}}{{\eta }_{4}},\quad {{h}_{{78}}} = - \eta _{4}^{'}{\text{/}}{{\eta }_{4}},$$
$${{h}_{{81}}} = 1,\quad {{h}_{{82}}} = {{\zeta }_{2}}{\text{/}}{{\zeta }_{1}}\quad {{h}_{{85}}} = - \zeta _{1}^{'}{\text{/}}{{\zeta }_{1}},\quad {{h}_{{86}}} = - \zeta _{2}^{'}{\text{/}}{{\zeta }_{1}},$$
Here now s = 1, 2; \({{s}_{{p4}}} = \frac{{{{S}_{p}}}}{{{{S}_{4}}}},(p = 1,2,3),s_{{r4}}^{'} = \frac{{S_{r}^{'}}}{{{{S}_{4}}}}\), (r = 1, 2, 3, 4), \(S_{{54}}^{'} = s_{{14}}^{'},S_{{64}}^{'} = s_{{24}}^{'}\), \(S_{{74}}^{'} = s_{{34}}^{'}\), \(S_{{84}}^{'} = s_{{44}}^{'}\), \({{D}_{3}} = - \left[ {\mu {\kern 1pt} '{\kern 1pt} \cos 2{{\theta }_{0}} - K{\kern 1pt} '{\kern 1pt} {{{\cos }}^{2}}{{\theta }_{0}} - \frac{{K{\kern 1pt} '{\kern 1pt} {{\eta }_{4}}}}{{l_{4}^{2}}}} \right],\)
$${{E}_{{1,2}}} = Q_{{1,2}}^{2}{{L}_{4}}\left[ {{{\lambda }_{2}} + {{\mu }_{2}} + \frac{{\beta _{0}^{'}{{\zeta }_{{1,2}}}}}{{l_{{1,2}}^{2}}} - \frac{{{{K}_{2}}\zeta _{{1,2}}^{2}}}{{l_{{1,2}}^{2}}}} \right]l_{{1,2}}^{3}\cos {{\theta }_{{1,2}}},$$
$${{E}_{3}} = Q_{3}^{2}{{L}_{4}}\left[ {{{\mu }_{2}} + {{K}_{2}} - \frac{{{{\eta }_{3}}}}{{l_{3}^{2}}}\left( {{{\gamma }_{2}}{{\eta }_{3}} + {{K}_{2}}} \right)} \right]l_{3}^{3}\cos {{\theta }_{3}},\quad {{E}_{4}} = - Q_{4}^{2},$$
$${{E}_{{5,6}}} = Q_{{5,6}}^{2}{{L}_{4}}\left[ {\lambda _{2}^{'} + \mu _{2}^{'} + \frac{{\beta _{0}^{{''}}\zeta _{2}^{'}}}{{l_{2}^{{'2}}}} - \frac{{K_{2}^{'}\zeta _{2}^{{'2}}}}{{l_{2}^{{'2}}}}} \right]l_{{1,2}}^{{'3}}\cos \theta _{{1,2}}^{'},$$
$${{E}_{{7,8}}} = Q_{{7,8}}^{2}{{L}_{4}}\left[ {(\mu _{2}^{'} + K_{2}^{'} - \frac{{{{\eta }_{{3,4}}}}}{{l_{{3,4}}^{{'2}}}}(\gamma _{2}^{'}\eta _{{3,4}}^{'} + K_{2}^{'})} \right]l_{{3,4}}^{{'3}}\cos \theta _{{3,4}}^{'},\quad {{L}_{4}} = {{\left[ {{{\mu }_{2}} + {{K}_{2}} - \frac{{{{\eta }_{4}}}}{{l_{4}^{2}}}\left( {{{\gamma }_{2}}{{\eta }_{4}} + {{K}_{2}}} \right)} \right]}^{{ - 1}}}.$$
