Luận án Nghiên cứu phương pháp xác định vị trí sự cố trên đường dây truyền tải điện thuộc lưới điện phức tạp
Định vị sự cố trên các đường dây truyển tải điện đã, đang và sẽ là một vấn đề kỹ thuật có tính thực tiễn cao trong quá trình vận hành hệ thống đường dây tải điện. Việc định vị chính xác, thậm chí giảm được sai số định vị sự cố cho phép rút ngắn được thời gian khắc phục sự cố, góp phần nâng cao độ tin cậy của hệ thống lưới điện truyền tải. Cho đến nay, hầu hết tất cả các rơ le kỹ thuật số đều sử dụng các biến thể của phương pháp tổng trở nhằm xác định vị trí sự cố trên đường dây tải điện, dựa trên bản ghi của rơ le từ một phía đầu đường dây. Về mặt toán học, đây là mô hình không chính xác, do tổng trở biểu kiến của rơ le phụ thuộc vào vị trí sự cố cũng như trào lưu công suất giữa hai phía đường dây trước khi xảy ra sự cố. Mặc dù mô hình tính toán không chính xác, các phương pháp dựa trên bản ghi sự cố một phía có tính thực tế cao, dễ áp dụng.
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)*cos(lc*x12)-(-cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3-
sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(lc*x11)*sin(lc*x12))*x6/(x5^2+x6^2))*v18+((cosh(db*x9-
lb*x9)*cos(db*x10-lb*x10)*x5-sinh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x6)*sinh(lc*x11)*cos(lc*x12)-(sinh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x5+cosh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x6)*cosh(lc*x11)*sin(lc*x12)+(-
sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*cosh(lc*x11)*cos(lc*x12)-(-cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3-
sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x4)*sinh(lc*x11)*sin(lc*x12))*i17-((sinh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x5+cosh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x6)*sinh(lc*x11)*cos(lc*x12)+(cosh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x5-
sinh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x6)*cosh(lc*x11)*sin(lc*x12)+(-cosh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x3-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(lc*x11)*cos(lc*x12)+(-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*sinh(lc*x11)*sin(lc*x12))*i18+(((sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x3-cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x4)*sinh(la*x7)*cos(la*x8)-
(cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3+sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(la*x7)*sin(la*x8))*x1/(x1^2+x2^2)+((cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x3+sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*sinh(la*x7)*cos(la*x8)+(sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x3-
cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*cosh(la*x7)*sin(la*x8))*x2/(x1^2+x2^2))*v13-(((cosh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x3+sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*sinh(la*x7)*cos(la*x8)+(sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x3-
cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x4)*cosh(la*x7)*sin(la*x8))*x1/(x1^2+x2^2)-
((sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x3-cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*sinh(la*x7)*cos(la*x8)-(cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x3+sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(la*x7)*sin(la*x8))*x2/(x1^2+x2^2))*v14+((-sinh(db*x9-
lb*x9)*cos(db*x10-lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*cosh(la*x7)*cos(la*x8)-(-cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3-
sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x4)*sinh(la*x7)*sin(la*x8))*i13-((-cosh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x3-sinh(db*x9-lb*x9)*cos(db*x10-
114
lb*x10)*x4)*cosh(la*x7)*cos(la*x8)+(-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x4)*sinh(la*x7)*sin(la*x8))*i14=0
f10(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12) = imag(PT5) = 0
f10 = sinh(db*x9)*sin(db*x10)*v15+cosh(db*x9)*cos(db*x10)*v16+(-cosh(db*x9)
*sin(db*x10)*x3-sinh(db*x9)*cos(db*x10)*x4)*i15+(-
sinh(db*x9)*cos(db*x10)*x3+cosh(db*x9)*sin(db*x10)*x4)*i16+(-sinh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*cosh(lc*x11)*cos(lc*x12)-cosh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*sinh(lc*x11)*sin(lc*x12)-((-cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3-
sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x4)*sinh(lc*x11)*cos(lc*x12)+(-sinh(db*x9-
lb*x9)*cos(db*x10-lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*cosh(lc*x11)*sin(lc*x12))*x5/(x5^2+x6^2)+((-sinh(db*x9-
lb*x9)*cos(db*x10-lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*sinh(lc*x11)*cos(lc*x12)-(-cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3-
sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(lc*x11)*sin(lc*x12))*x6/(x5^2+x6^2))*v17+(-cosh(db*x9-
lb*x9)*cos(db*x10-lb*x10)*cosh(lc*x11)*cos(lc*x12)+sinh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*sinh(lc*x11)*sin(lc*x12)-((-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x4)*sinh(lc*x11)*cos(lc*x12)-(-
cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(lc*x11)*sin(lc*x12))*x5/(x5^2+x6^2)-((-cosh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x3-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*sinh(lc*x11)*cos(lc*x12)+(-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*cosh(lc*x11)*sin(lc*x12))*x6/(x5^2+x6^2))*v18+((sinh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x5+cosh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x6)*sinh(lc*x11)*cos(lc*x12)+(cosh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x5-
sinh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x6)*cosh(lc*x11)*sin(lc*x12)+(-cosh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x3-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(lc*x11)*cos(lc*x12)+(-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*sinh(lc*x11)*sin(lc*x12))*i17+((cosh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x5-
sinh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x6)*sinh(lc*x11)*cos(lc*x12)-(sinh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x5+cosh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x6)*cosh(lc*x11)*sin(lc*x12)+(-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x4)*cosh(lc*x11)*cos(lc*x12)-(-
cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*sinh(lc*x11)*sin(lc*x12))*i18+(((cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x3+sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*sinh(la*x7)*cos(la*x8)+(sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x3-
cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x4)*cosh(la*x7)*sin(la*x8))*x1/(x1^2+x2^2)-
((sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x3-cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*sinh(la*x7)*cos(la*x8)-(cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x3+sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(la*x7)*sin(la*x8))*x2/(x1^2+x2^2))*v13+(((sinh(db*x9-
lb*x9)*cos(db*x10-lb*x10)*x3-cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*sinh(la*x7)*cos(la*x8)-(cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x3+sinh(db*x9-lb*x9)*cos(db*x10-
115
lb*x10)*x4)*cosh(la*x7)*sin(la*x8))*x1/(x1^2+x2^2)+((cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x3+sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*sinh(la*x7)*cos(la*x8)+(sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x3-
cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*cosh(la*x7)*sin(la*x8))*x2/(x1^2+x2^2))*v14+((-cosh(db*x9-
lb*x9)*sin(db*x10-lb*x10)*x3-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x4)*cosh(la*x7)*cos(la*x8)+(-sinh(db*x9-lb*x9)*cos(db*x10-
lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x4)*sinh(la*x7)*sin(la*x8))*i13+((-
sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x3+cosh(db*x9-lb*x9)*sin(db*x10-
lb*x10)*x4)*cosh(la*x7)*cos(la*x8)-(-cosh(db*x9-lb*x9)*sin(db*x10-lb*x10)*x3-
sinh(db*x9-lb*x9)*cos(db*x10-lb*x10)*x4)*sinh(la*x7)*sin(la*x8))*i14=0
f111(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12) = real(PT6) = 0
f11 = cosh(dc*x11)*cos(dc*x12)*v23-sinh(dc*x11)*sin(dc*x12)*v24+(-sinh(dc*x11)
*cos(dc*x12)*x5+cosh(dc*x11)*sin(dc*x12)*x6)*i23-(-cosh(dc*x11)*sin(dc*x12)*x5-
sinh(dc*x11)*cos(dc*x12)*x6)*i24+(-cosh(la*x7)*cos(la*x8)*cosh(dc*x11-
lc*x11)*cos(dc*x12-lc*x12)+sinh(la*x7)*sin(la*x8)*sinh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)-((-sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5+cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x6)*sinh(la*x7)*cos(la*x8)-(-cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(la*x7)*sin(la*x8))*x1/(x1^2+x2^2)-((-cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(la*x7)*cos(la*x8)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*cosh(la*x7)*sin(la*x8))*x2/(x1^2+x2^2))*v19-(-
sinh(la*x7)*sin(la*x8)*cosh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)-
cosh(la*x7)*cos(la*x8)*sinh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)-((-cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(la*x7)*cos(la*x8)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*cosh(la*x7)*sin(la*x8))*x1/(x1^2+x2^2)+((-sinh(dc*x11-
lc*x11)*cos(dc*x12-lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(la*x7)*cos(la*x8)-(-cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-
sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(la*x7)*sin(la*x8))*x2/(x1^2+x2^2))*v20+((cosh(dc*x11-
lc*x11)*cos(dc*x12-lc*x12)*x1-sinh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x2)*sinh(la*x7)*cos(la*x8)-(sinh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x1+cosh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x2)*cosh(la*x7)*sin(la*x8)+(-
sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*cosh(la*x7)*cos(la*x8)-(-cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-
sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x6)*sinh(la*x7)*sin(la*x8))*i19-((sinh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x1+cosh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x2)*sinh(la*x7)*cos(la*x8)+(cosh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x1-
sinh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x2)*cosh(la*x7)*sin(la*x8)+(-cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(la*x7)*cos(la*x8)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(la*x7)*sin(la*x8))*i20+(((sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5-
116
cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x6)*sinh(lb*x9)*cos(lb*x10)-(cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5+sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*sin(lb*x10))*x3/(x3^2+x4^2)+((cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5+sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*cos(lb*x10)+(sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5-
cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*sin(lb*x10))*x4/(x3^2+x4^2))*v21-(((cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5+sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*cos(lb*x10)+(sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5-
cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x6)*cosh(lb*x9)*sin(lb*x10))*x3/(x3^2+x4^2)-
((sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5-cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*cos(lb*x10)-(cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x5+sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*sin(lb*x10))*x4/(x3^2+x4^2))*v22+((-sinh(dc*x11-
lc*x11)*cos(dc*x12-lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*cos(lb*x10)-(-cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-
sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x6)*sinh(lb*x9)*sin(lb*x10))*i21-((-
cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*cos(lb*x10)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*sin(lb*x10))*i22=0
f12(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12) = imag(PT6) = 0
f12 = sinh(dc*x11)*sin(dc*x12)*v23+cosh(dc*x11)*cos(dc*x12)*v24+(-cosh(dc*x11)
*sin(dc*x12)*x5-sinh(dc*x11)*cos(dc*x12)*x6)*i23+(-
sinh(dc*x11)*cos(dc*x12)*x5+cosh(dc*x11)*sin(dc*x12)*x6)*i24+(-
sinh(la*x7)*sin(la*x8)*cosh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)-
cosh(la*x7)*cos(la*x8)*sinh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)-((-cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(la*x7)*cos(la*x8)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*cosh(la*x7)*sin(la*x8))*x1/(x1^2+x2^2)+((-sinh(dc*x11-
lc*x11)*cos(dc*x12-lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(la*x7)*cos(la*x8)-(-cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-
sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(la*x7)*sin(la*x8))*x2/(x1^2+x2^2))*v19+(-
cosh(la*x7)*cos(la*x8)*cosh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)+sinh(la*x7)*sin(la*x8)*sinh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)-((-sinh(dc*x11-
lc*x11)*cos(dc*x12-lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(la*x7)*cos(la*x8)-(-cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-
sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x6)*cosh(la*x7)*sin(la*x8))*x1/(x1^2+x2^2)-
((-cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(la*x7)*cos(la*x8)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*cosh(la*x7)*sin(la*x8))*x2/(x1^2+x2^2))*v20+((sinh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x1+cosh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x2)*sinh(la*x7)*cos(la*x8)+(cosh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x1-
sinh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x2)*cosh(la*x7)*sin(la*x8)+(-cosh(dc*x11-
117
lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(la*x7)*cos(la*x8)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(la*x7)*sin(la*x8))*i19+((cosh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x1-
sinh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x2)*sinh(la*x7)*cos(la*x8)-(sinh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x1+cosh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x2)*cosh(la*x7)*sin(la*x8)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x6)*cosh(la*x7)*cos(la*x8)-(-
cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(la*x7)*sin(la*x8))*i20+(((cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x5+sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*cos(lb*x10)+(sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5-
cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x6)*cosh(lb*x9)*sin(lb*x10))*x3/(x3^2+x4^2)-
((sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5-cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*cos(lb*x10)-(cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x5+sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*sin(lb*x10))*x4/(x3^2+x4^2))*v21+(((sinh(dc*x11-
lc*x11)*cos(dc*x12-lc*x12)*x5-cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*cos(lb*x10)-(cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x5+sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*sin(lb*x10))*x3/(x3^2+x4^2)+((cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5+sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*cos(lb*x10)+(sinh(dc*x11-lc*x11)*cos(dc*x12-lc*x12)*x5-
cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*sin(lb*x10))*x4/(x3^2+x4^2))*v22+((-cosh(dc*x11-
lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*cosh(lb*x9)*cos(lb*x10)+(-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*sin(lb*x10))*i21+((-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x5+cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x6)*cosh(lb*x9)*cos(lb*x10)-(-
cosh(dc*x11-lc*x11)*sin(dc*x12-lc*x12)*x5-sinh(dc*x11-lc*x11)*cos(dc*x12-
lc*x12)*x6)*sinh(lb*x9)*sin(lb*x10))*i22=0
A.7. Phương trình (3.105)
f1(x1,x2,x3,x4,x5,x6,x7,x8) = real(PT1) = 0
f1 = v1+(-cosh(la*x5)*cos(la*x6)*cosh(lb*x7)*cos(lb*x8)+sinh(la*x5)*sin(la*x6)
*sinh(lb*x7)*sin(lb*x8)-((x1*sinh(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*cos(lb*x8)-
(x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*sin(lb*x8))*x3/(x3^
2+x4^2)-
((x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*cos(lb*x8)+(x1*sin
h(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*sin(lb*x8))*x4/(x3^2+x4^2))*v3-(-
sinh(la*x5)*sin(la*x6)*cosh(lb*x7)*cos(lb*x8)-
cosh(la*x5)*cos(la*x6)*sinh(lb*x7)*sin(lb*x8)-
((x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*cos(lb*x8)+(x1*sin
118
h(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*sin(lb*x8))*x3/(x3^2+x4^2)+((x1*sinh(la*x5)*c
os(la*x6)-x2*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*cos(lb*x8)-
(x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*sin(lb*x8))*x4/(x3^
2+x4^2))*v4+((cosh(la*x5)*cos(la*x6)*x3-
sinh(la*x5)*sin(la*x6)*x4)*sinh(lb*x7)*cos(lb*x8)-
(sinh(la*x5)*sin(la*x6)*x3+cosh(la*x5)*cos(la*x6)*x4)*cosh(lb*x7)*sin(lb*x8)+(x1*sin
h(la*x5)*cos(la*x6)-x2*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*cos(lb*x8)-
(x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*sin(lb*x8))*i3-
((sinh(la*x5)*sin(la*x6)*x3+cosh(la*x5)*cos(la*x6)*x4)*sinh(lb*x7)*cos(lb*x8)+(cosh(l
a*x5)*cos(la*x6)*x3-
sinh(la*x5)*sin(la*x6)*x4)*cosh(lb*x7)*sin(lb*x8)+(x2*sinh(la*x5)*cos(la*x6)+x1*cosh
(la*x5)*sin(la*x6))*cosh(lb*x7)*cos(lb*x8)+(x1*sinh(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*sin(lb*x8))*i4+(-
sinh(la*x5)*cos(la*x6)*sinh(lc*x5)*cos(lc*x6)+cosh(la*x5)*sin(la*x6)*cosh(lc*x5)*sin(l
c*x6))*v5-(-cosh(la*x5)*sin(la*x6)*sinh(lc*x5)*cos(lc*x6)-
sinh(la*x5)*cos(la*x6)*cosh(lc*x5)*sin(lc*x6))*v6+((x1*sinh(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*cosh(lc*x5)*cos(lc*x6)-
(x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*sinh(lc*x5)*sin(lc*x6))*i5-
((x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*cosh(lc*x5)*cos(lc*x6)+(x1*sin
h(la*x5)*cos(la*x6)-x2*cosh(la*x5)*sin(la*x6))*sinh(lc*x5)*sin(lc*x6))*i6=0
f2(x1,x2,x3,x4,x5,x6,x7,x8) = imag (PT1) = 0
f2 = v2+(-sinh(la*x5)*sin(la*x6)*cosh(lb*x7)*cos(lb*x8)-cosh(la*x5)*cos(la*x6)
*sinh(lb*x7)*sin(lb*x8)-
((x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*cos(lb*x8)+(x1*sin
h(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*sin(lb*x8))*x3/(x3^2+x4^2)+((x1*sinh(la*x5)*c
os(la*x6)-x2*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*cos(lb*x8)-
(x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*sin(lb*x8))*x4/(x3^
2+x4^2))*v3+(-
cosh(la*x5)*cos(la*x6)*cosh(lb*x7)*cos(lb*x8)+sinh(la*x5)*sin(la*x6)*sinh(lb*x7)*sin(l
b*x8)-((x1*sinh(la*x5)*cos(la*x6)-x2*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*cos(lb*x8)-
(x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*sin(lb*x8))*x3/(x3^
2+x4^2)-
((x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*cos(lb*x8)+(x1*sin
h(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*sin(lb*x8))*x4/(x3^2+x4^2))*v4+((sinh(la*x5)*s
in(la*x6)*x3+cosh(la*x5)*cos(la*x6)*x4)*sinh(lb*x7)*cos(lb*x8)+(cosh(la*x5)*cos(la*x
6)*x3-
sinh(la*x5)*sin(la*x6)*x4)*cosh(lb*x7)*sin(lb*x8)+(x2*sinh(la*x5)*cos(la*x6)+x1*cosh
(la*x5)*sin(la*x6))*cosh(lb*x7)*cos(lb*x8)+(x1*sinh(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*sin(lb*x8))*i3+((cosh(la*x5)*cos(la*x6)*x3-
sinh(la*x5)*sin(la*x6)*x4)*sinh(lb*x7)*cos(lb*x8)-
(sinh(la*x5)*sin(la*x6)*x3+cosh(la*x5)*cos(la*x6)*x4)*cosh(lb*x7)*sin(lb*x8)+(x1*sin
h(la*x5)*cos(la*x6)-x2*cosh(la*x5)*sin(la*x6))*cosh(lb*x7)*cos(lb*x8)-
(x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*sinh(lb*x7)*sin(lb*x8))*i4+(-
cosh(la*x5)*sin(la*x6)*sinh(lc*x5)*cos(lc*x6)-
119
sinh(la*x5)*cos(la*x6)*cosh(lc*x5)*sin(lc*x6))*v5+(-
sinh(la*x5)*cos(la*x6)*sinh(lc*x5)*cos(lc*x6)+cosh(la*x5)*sin(la*x6)*cosh(lc*x5)*sin(l
c*x6))*v6+((x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*cosh(lc*x5)*cos(lc*
x6)+(x1*sinh(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*sinh(lc*x5)*sin(lc*x6))*i5+((x1*sinh(la*x5)*cos(la*x6)-
x2*cosh(la*x5)*sin(la*x6))*cosh(lc*x5)*cos(lc*x6)-
(x2*sinh(la*x5)*cos(la*x6)+x1*cosh(la*x5)*sin(la*x6))*sinh(lc*x5)*sin(lc*x6))*i6=0
f3(x1,x2,x3,x4,x5,x6,x7,x8) = real(PT2) = 0
f3 = v3+(-cosh(lb*x7)*cos(lb*x8)*cosh(lc*x5)*cos(lc*x6)+sinh(lb*x7)*sin(lb*x8)
*sinh(lc*x5)*sin(lc*x6)-((x3*sinh(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*cos(lc*x6)-
(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*sin(lc*x6))*x1/(x1^
2+x2^2)-
((x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*cos(lc*x6)+(x3*sin
h(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*sin(lc*x6))*x2/(x1^2+x2^2))*v5-(-
sinh(lb*x7)*sin(lb*x8)*cosh(lc*x5)*cos(lc*x6)-
cosh(lb*x7)*cos(lb*x8)*sinh(lc*x5)*sin(lc*x6)-
((x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*cos(lc*x6)+(x3*sin
h(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*sin(lc*x6))*x1/(x1^2+x2^2)+((x3*sinh(lb*x7)*c
os(lb*x8)-x4*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*cos(lc*x6)-
(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*sin(lc*x6))*x2/(x1^
2+x2^2))*v6+((cosh(lb*x7)*cos(lb*x8)*x1-
sinh(lb*x7)*sin(lb*x8)*x2)*sinh(lc*x5)*cos(lc*x6)-
(sinh(lb*x7)*sin(lb*x8)*x1+cosh(lb*x7)*cos(lb*x8)*x2)*cosh(lc*x5)*sin(lc*x6)+(x3*sinh
(lb*x7)*cos(lb*x8)-x4*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*cos(lc*x6)-
(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*sin(lc*x6))*i5-
((sinh(lb*x7)*sin(lb*x8)*x1+cosh(lb*x7)*cos(lb*x8)*x2)*sinh(lc*x5)*cos(lc*x6)+(cosh(l
b*x7)*cos(lb*x8)*x1-
sinh(lb*x7)*sin(lb*x8)*x2)*cosh(lc*x5)*sin(lc*x6)+(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(
lb*x7)*sin(lb*x8))*cosh(lc*x5)*cos(lc*x6)+(x3*sinh(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*sin(lc*x6))*i6+(((-
x3*sinh(lb*x7)*cos(lb*x8)+x4*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*cos(la*x6)-(-
x4*sinh(lb*x7)*cos(lb*x8)-
x3*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*sin(la*x6))*x1/(x1^2+x2^2)+((-
x4*sinh(lb*x7)*cos(lb*x8)-x3*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*cos(la*x6)+(-
x3*sinh(lb*x7)*cos(lb*x8)+x4*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*sin(la*x6))*x2/(x1^2
+x2^2))*v1-(((-x4*sinh(lb*x7)*cos(lb*x8)-
x3*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*cos(la*x6)+(-
x3*sinh(lb*x7)*cos(lb*x8)+x4*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*sin(la*x6))*x1/(x1^2
+x2^2)-((-
x3*sinh(lb*x7)*cos(lb*x8)+x4*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*cos(la*x6)-(-
x4*sinh(lb*x7)*cos(lb*x8)-
x3*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*sin(la*x6))*x2/(x1^2+x2^2))*v2+((x3*sinh(lb*x
7)*cos(lb*x8)-x4*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*cos(la*x6)-
(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*sin(la*x6))*i1-
120
((x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*cos(la*x6)+(x3*si
nh(lb*x7)*cos(lb*x8)-x4*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*sin(la*x6))*i2=0
f4(x1,x2,x3,x4,x5,x6,x7,x8) = imag (PT2) = 0
f4 = v4+(-sinh(lb*x7)*sin(lb*x8)*cosh(lc*x5)*cos(lc*x6)-cosh(lb*x7)*cos(lb*x8)
*sinh(lc*x5)*sin(lc*x6)-
((x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*cos(lc*x6)+(x3*sin
h(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*sin(lc*x6))*x1/(x1^2+x2^2)+((x3*sinh(lb*x7)*c
os(lb*x8)-x4*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*cos(lc*x6)-
(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*sin(lc*x6))*x2/(x1^
2+x2^2))*v5+(-
cosh(lb*x7)*cos(lb*x8)*cosh(lc*x5)*cos(lc*x6)+sinh(lb*x7)*sin(lb*x8)*sinh(lc*x5)*sin(l
c*x6)-((x3*sinh(lb*x7)*cos(lb*x8)-x4*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*cos(lc*x6)-
(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*sin(lc*x6))*x1/(x1^
2+x2^2)-
((x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*cos(lc*x6)+(x3*sin
h(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*sin(lc*x6))*x2/(x1^2+x2^2))*v6+((sinh(lb*x7)*s
in(lb*x8)*x1+cosh(lb*x7)*cos(lb*x8)*x2)*sinh(lc*x5)*cos(lc*x6)+(cosh(lb*x7)*cos(lb*x
8)*x1-
sinh(lb*x7)*sin(lb*x8)*x2)*cosh(lc*x5)*sin(lc*x6)+(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(
lb*x7)*sin(lb*x8))*cosh(lc*x5)*cos(lc*x6)+(x3*sinh(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*sin(lc*x6))*i5+((cosh(lb*x7)*cos(lb*x8)*x1-
sinh(lb*x7)*sin(lb*x8)*x2)*sinh(lc*x5)*cos(lc*x6)-
(sinh(lb*x7)*sin(lb*x8)*x1+cosh(lb*x7)*cos(lb*x8)*x2)*cosh(lc*x5)*sin(lc*x6)+(x3*sinh
(lb*x7)*cos(lb*x8)-x4*cosh(lb*x7)*sin(lb*x8))*cosh(lc*x5)*cos(lc*x6)-
(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*sinh(lc*x5)*sin(lc*x6))*i6+(((-
x4*sinh(lb*x7)*cos(lb*x8)-x3*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*cos(la*x6)+(-
x3*sinh(lb*x7)*cos(lb*x8)+x4*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*sin(la*x6))*x1/(x1^2
+x2^2)-((-
x3*sinh(lb*x7)*cos(lb*x8)+x4*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*cos(la*x6)-(-
x4*sinh(lb*x7)*cos(lb*x8)-
x3*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*sin(la*x6))*x2/(x1^2+x2^2))*v1+(((-
x3*sinh(lb*x7)*cos(lb*x8)+x4*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*cos(la*x6)-(-
x4*sinh(lb*x7)*cos(lb*x8)-
x3*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*sin(la*x6))*x1/(x1^2+x2^2)+((-
x4*sinh(lb*x7)*cos(lb*x8)-x3*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*cos(la*x6)+(-
x3*sinh(lb*x7)*cos(lb*x8)+x4*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*sin(la*x6))*x2/(x1^2
+x2^2))*v2+((x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*cos(la
*x6)+(x3*sinh(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*sin(la*x6))*i1+((x3*sinh(lb*x7)*cos(lb*x8)-
x4*cosh(lb*x7)*sin(lb*x8))*cosh(la*x5)*cos(la*x6)-
(x4*sinh(lb*x7)*cos(lb*x8)+x3*cosh(lb*x7)*sin(lb*x8))*sinh(la*x5)*sin(la*x6))*i2=0
f5(x1,x2,x3,x4,x5,x6,x7,x8) = real(PT4) = 0
f5 = cosh(da*x5)*cos(da*x6)*v7-sinh(da*x5)*sin(da*x6)*v8+(-sinh(da*x5)*cos(da*x6)
*x1+cosh(da*x5)*sin(da*x6)*x2)*i7-(-cosh(da*x5)*sin(da*x6)*x1-
121
sinh(da*x5)*cos(da*x6)*x2)*i8+(-cosh(da*x5-la*x5)*cos(da*x6-
la*x6)*cosh(lb*x7)*cos(lb*x8)+sinh(da*x5-la*x5)*sin(da*x6-
la*x6)*sinh(lb*x7)*sin(lb*x8)-((-sinh(da*x5-la*x5)*cos(da*x6-la*x6)*x1+cosh(da*x5-
la*x5)*sin(da*x6-la*x6)*x2)*sinh(lb*x7)*cos(lb*x8)-(-cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*cosh(lb*x7)*sin(lb*x8))*x3/(x3^2+x4^2)-((-cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-la*x6)*x2)*sinh(lb*x7)*cos(lb*x8)+(-
sinh(da*x5-la*x5)*cos(da*x6-la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x2)*cosh(lb*x7)*sin(lb*x8))*x4/(x3^2+x4^2))*v9-(-sinh(da*x5-la*x5)*sin(da*x6-
la*x6)*cosh(lb*x7)*cos(lb*x8)-cosh(da*x5-la*x5)*cos(da*x6-
la*x6)*sinh(lb*x7)*sin(lb*x8)-((-cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-
la*x5)*cos(da*x6-la*x6)*x2)*sinh(lb*x7)*cos(lb*x8)+(-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x2)*cosh(lb*x7)*sin(lb*x8))*x3/(x3^2+x4^2)+((-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x2)*sinh(lb*x7)*cos(lb*x8)-(-
cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*cosh(lb*x7)*sin(lb*x8))*x4/(x3^2+x4^2))*v10+((cosh(da*x5-
la*x5)*cos(da*x6-la*x6)*x3-sinh(da*x5-la*x5)*sin(da*x6-
la*x6)*x4)*sinh(lb*x7)*cos(lb*x8)-(sinh(da*x5-la*x5)*sin(da*x6-la*x6)*x3+cosh(da*x5-
la*x5)*cos(da*x6-la*x6)*x4)*cosh(lb*x7)*sin(lb*x8)+(-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x2)*cosh(lb*x7)*cos(lb*x8)-(-
cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*sinh(lb*x7)*sin(lb*x8))*i9-((sinh(da*x5-la*x5)*sin(da*x6-
la*x6)*x3+cosh(da*x5-la*x5)*cos(da*x6-
la*x6)*x4)*sinh(lb*x7)*cos(lb*x8)+(cosh(da*x5-la*x5)*cos(da*x6-la*x6)*x3-
sinh(da*x5-la*x5)*sin(da*x6-la*x6)*x4)*cosh(lb*x7)*sin(lb*x8)+(-cosh(da*x5-
la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*cosh(lb*x7)*cos(lb*x8)+(-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x2)*sinh(lb*x7)*sin(lb*x8))*i10+(sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*sinh(lc*x5)*cos(lc*x6)-cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*cosh(lc*x5)*sin(lc*x6))*v11-(cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*sinh(lc*x5)*cos(lc*x6)+sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*cosh(lc*x5)*sin(lc*x6))*v12+((-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x2)*cosh(lc*x5)*cos(lc*x6)-(-
cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*sinh(lc*x5)*sin(lc*x6))*i11-((-cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-
sinh(da*x5-la*x5)*cos(da*x6-la*x6)*x2)*cosh(lc*x5)*cos(lc*x6)+(-sinh(da*x5-
la*x5)*cos(da*x6-la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x2)*sinh(lc*x5)*sin(lc*x6))*i12=0
f6(x1,x2,x3,x4,x5,x6,x7,x8) = imag (PT4) = 0
f6 = sinh(da*x5)*sin(da*x6)*v7+cosh(da*x5)*cos(da*x6)*v8+(-cosh(da*x5)*sin(da*x6)
*x1-sinh(da*x5)*cos(da*x6)*x2)*i7+(-
sinh(da*x5)*cos(da*x6)*x1+cosh(da*x5)*sin(da*x6)*x2)*i8+(-sinh(da*x5-
la*x5)*sin(da*x6-la*x6)*cosh(lb*x7)*cos(lb*x8)-cosh(da*x5-la*x5)*cos(da*x6-
la*x6)*sinh(lb*x7)*sin(lb*x8)-((-cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-
la*x5)*cos(da*x6-la*x6)*x2)*sinh(lb*x7)*cos(lb*x8)+(-sinh(da*x5-la*x5)*cos(da*x6-
122
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x2)*cosh(lb*x7)*sin(lb*x8))*x3/(x3^2+x4^2)+((-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x2)*sinh(lb*x7)*cos(lb*x8)-(-
cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*cosh(lb*x7)*sin(lb*x8))*x4/(x3^2+x4^2))*v9+(-cosh(da*x5-
la*x5)*cos(da*x6-la*x6)*cosh(lb*x7)*cos(lb*x8)+sinh(da*x5-la*x5)*sin(da*x6-
la*x6)*sinh(lb*x7)*sin(lb*x8)-((-sinh(da*x5-la*x5)*cos(da*x6-la*x6)*x1+cosh(da*x5-
la*x5)*sin(da*x6-la*x6)*x2)*sinh(lb*x7)*cos(lb*x8)-(-cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*cosh(lb*x7)*sin(lb*x8))*x3/(x3^2+x4^2)-((-cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-la*x6)*x2)*sinh(lb*x7)*cos(lb*x8)+(-
sinh(da*x5-la*x5)*cos(da*x6-la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x2)*cosh(lb*x7)*sin(lb*x8))*x4/(x3^2+x4^2))*v10+((sinh(da*x5-
la*x5)*sin(da*x6-la*x6)*x3+cosh(da*x5-la*x5)*cos(da*x6-
la*x6)*x4)*sinh(lb*x7)*cos(lb*x8)+(cosh(da*x5-la*x5)*cos(da*x6-la*x6)*x3-
sinh(da*x5-la*x5)*sin(da*x6-la*x6)*x4)*cosh(lb*x7)*sin(lb*x8)+(-cosh(da*x5-
la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*cosh(lb*x7)*cos(lb*x8)+(-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x2)*sinh(lb*x7)*sin(lb*x8))*i9+((cosh(da*x5-la*x5)*cos(da*x6-la*x6)*x3-
sinh(da*x5-la*x5)*sin(da*x6-la*x6)*x4)*sinh(lb*x7)*cos(lb*x8)-(sinh(da*x5-
la*x5)*sin(da*x6-la*x6)*x3+cosh(da*x5-la*x5)*cos(da*x6-
la*x6)*x4)*cosh(lb*x7)*sin(lb*x8)+(-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x2)*cosh(lb*x7)*cos(lb*x8)-(-
cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*sinh(lb*x7)*sin(lb*x8))*i10+(cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*sinh(lc*x5)*cos(lc*x6)+sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*cosh(lc*x5)*sin(lc*x6))*v11+(sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*sinh(lc*x5)*cos(lc*x6)-cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*cosh(lc*x5)*sin(lc*x6))*v12+((-cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-
sinh(da*x5-la*x5)*cos(da*x6-la*x6)*x2)*cosh(lc*x5)*cos(lc*x6)+(-sinh(da*x5-
la*x5)*cos(da*x6-la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-
la*x6)*x2)*sinh(lc*x5)*sin(lc*x6))*i11+((-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x1+cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x2)*cosh(lc*x5)*cos(lc*x6)-(-
cosh(da*x5-la*x5)*sin(da*x6-la*x6)*x1-sinh(da*x5-la*x5)*cos(da*x6-
la*x6)*x2)*sinh(lc*x5)*sin(lc*x6))*i12=0
f7(x1,x2,x3,x4,x5,x6,x7,x8) = real(PT5) = 0
f7 = cosh(db*x7)*cos(db*x8)*v15-sinh(db*x7)*sin(db*x8)*v16+(-sinh(db*x7)
*cos(db*x8)*x3+cosh(db*x7)*sin(db*x8)*x4)*i15-(-cosh(db*x7)*sin(db*x8)*x3-
sinh(db*x7)*cos(db*x8)*x4)*i16+(-cosh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*cosh(lc*x5)*cos(lc*x6)+sinh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*sinh(lc*x5)*sin(lc*x6)-((-sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3+cosh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x4)*sinh(lc*x5)*cos(lc*x6)-(-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*cosh(lc*x5)*sin(lc*x6))*x1/(x1^2+x2^2)-((-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x4)*sinh(lc*x5)*cos(lc*x6)+(-
sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-
123
lb*x8)*x4)*cosh(lc*x5)*sin(lc*x6))*x2/(x1^2+x2^2))*v17-(-sinh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*cosh(lc*x5)*cos(lc*x6)-cosh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*sinh(lc*x5)*sin(lc*x6)-((-cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3-sinh(db*x7-
lb*x7)*cos(db*x8-lb*x8)*x4)*sinh(lc*x5)*cos(lc*x6)+(-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*cosh(lc*x5)*sin(lc*x6))*x1/(x1^2+x2^2)+((-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*sinh(lc*x5)*cos(lc*x6)-(-
cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*cosh(lc*x5)*sin(lc*x6))*x2/(x1^2+x2^2))*v18+((cosh(db*x7-
lb*x7)*cos(db*x8-lb*x8)*x1-sinh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x2)*sinh(lc*x5)*cos(lc*x6)-(sinh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x1+cosh(db*x7-
lb*x7)*cos(db*x8-lb*x8)*x2)*cosh(lc*x5)*sin(lc*x6)+(-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*cosh(lc*x5)*cos(lc*x6)-(-
cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*sinh(lc*x5)*sin(lc*x6))*i17-((sinh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x1+cosh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x2)*sinh(lc*x5)*cos(lc*x6)+(cosh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x1-sinh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x2)*cosh(lc*x5)*sin(lc*x6)+(-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x4)*cosh(lc*x5)*cos(lc*x6)+(-
sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*sinh(lc*x5)*sin(lc*x6))*i18+(((sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3-
cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*sinh(la*x5)*cos(la*x6)-(cosh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x3+sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*cosh(la*x5)*sin(la*x6))*x1/(x1^2+x2^2)+((cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x3+sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*sinh(la*x5)*cos(la*x6)+(sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3-
cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*cosh(la*x5)*sin(la*x6))*x2/(x1^2+x2^2))*v13-
(((cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3+sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*sinh(la*x5)*cos(la*x6)+(sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3-
cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*cosh(la*x5)*sin(la*x6))*x1/(x1^2+x2^2)-
((sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*sinh(la*x5)*cos(la*x6)-(cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3+sinh(db*x7-
lb*x7)*cos(db*x8-lb*x8)*x4)*cosh(la*x5)*sin(la*x6))*x2/(x1^2+x2^2))*v14+((-
sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*cosh(la*x5)*cos(la*x6)-(-cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3-
sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x4)*sinh(la*x5)*sin(la*x6))*i13-((-cosh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*cosh(la*x5)*cos(la*x6)+(-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*sinh(la*x5)*sin(la*x6))*i14=0
f8(x1,x2,x3,x4,x5,x6,x7,x8) = imag(PT5) = 0
f8 = sinh(db*x7)*sin(db*x8)*v15+cosh(db*x7)*cos(db*x8)*v16+(-cosh(db*x7)
*sin(db*x8)*x3-sinh(db*x7)*cos(db*x8)*x4)*i15+(-
sinh(db*x7)*cos(db*x8)*x3+cosh(db*x7)*sin(db*x8)*x4)*i16+(-sinh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*cosh(lc*x5)*cos(lc*x6)-cosh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*sinh(lc*x5)*sin(lc*x6)-((-cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3-sinh(db*x7-
lb*x7)*cos(db*x8-lb*x8)*x4)*sinh(lc*x5)*cos(lc*x6)+(-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-
124
lb*x8)*x4)*cosh(lc*x5)*sin(lc*x6))*x1/(x1^2+x2^2)+((-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*sinh(lc*x5)*cos(lc*x6)-(-
cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*cosh(lc*x5)*sin(lc*x6))*x2/(x1^2+x2^2))*v17+(-cosh(db*x7-
lb*x7)*cos(db*x8-lb*x8)*cosh(lc*x5)*cos(lc*x6)+sinh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*sinh(lc*x5)*sin(lc*x6)-((-sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3+cosh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x4)*sinh(lc*x5)*cos(lc*x6)-(-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*cosh(lc*x5)*sin(lc*x6))*x1/(x1^2+x2^2)-((-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x4)*sinh(lc*x5)*cos(lc*x6)+(-
sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*cosh(lc*x5)*sin(lc*x6))*x2/(x1^2+x2^2))*v18+((sinh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x1+cosh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x2)*sinh(lc*x5)*cos(lc*x6)+(cosh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x1-sinh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x2)*cosh(lc*x5)*sin(lc*x6)+(-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x4)*cosh(lc*x5)*cos(lc*x6)+(-
sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*sinh(lc*x5)*sin(lc*x6))*i17+((cosh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x1-
sinh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x2)*sinh(lc*x5)*cos(lc*x6)-(sinh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x1+cosh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x2)*cosh(lc*x5)*sin(lc*x6)+(-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*cosh(lc*x5)*cos(lc*x6)-(-
cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*sinh(lc*x5)*sin(lc*x6))*i18+(((cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x3+sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*sinh(la*x5)*cos(la*x6)+(sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3-
cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*cosh(la*x5)*sin(la*x6))*x1/(x1^2+x2^2)-
((sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*sinh(la*x5)*cos(la*x6)-(cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3+sinh(db*x7-
lb*x7)*cos(db*x8-
lb*x8)*x4)*cosh(la*x5)*sin(la*x6))*x2/(x1^2+x2^2))*v13+(((sinh(db*x7-
lb*x7)*cos(db*x8-lb*x8)*x3-cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*sinh(la*x5)*cos(la*x6)-(cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3+sinh(db*x7-
lb*x7)*cos(db*x8-lb*x8)*x4)*cosh(la*x5)*sin(la*x6))*x1/(x1^2+x2^2)+((cosh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x3+sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*sinh(la*x5)*cos(la*x6)+(sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3-
cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*cosh(la*x5)*sin(la*x6))*x2/(x1^2+x2^2))*v14+((-cosh(db*x7-
lb*x7)*sin(db*x8-lb*x8)*x3-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x4)*cosh(la*x5)*cos(la*x6)+(-sinh(db*x7-lb*x7)*cos(db*x8-
lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x4)*sinh(la*x5)*sin(la*x6))*i13+((-
sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x3+cosh(db*x7-lb*x7)*sin(db*x8-
lb*x8)*x4)*cosh(la*x5)*cos(la*x6)-(-cosh(db*x7-lb*x7)*sin(db*x8-lb*x8)*x3-
sinh(db*x7-lb*x7)*cos(db*x8-lb*x8)*x4)*sinh(la*x5)*sin(la*x6))*i14=0
125
A.8. Phương trình (3.111)
f1(x1,x2,x3,x4,x5) = real(PT1) = 0
f1 = v1-(cosh(la*x3)*cos(la*x4)*cosh(lb*x3)*cos(lb*x4)-
sinh(la*x3)*sin(la*x4)*sinh(lb*x3)*sin(lb*x4)+sinh(la*x3)*cos(la*x4)*sinh(lb*x3)*cos(l
b*x4)-
cosh(la*x3)*sin(la*x4)*cosh(lb*x3)*sin(lb*x4))*v3+(sinh(la*x3)*sin(la*x4)*cosh(lb*x3)
*cos(lb*x4)+cosh(la*x3)*cos(la*x4)*sinh(lb*x3)*sin(lb*x4)+cosh(la*x3)*sin(la*x4)*sinh
(lb*x3)*cos(lb*x4)+sinh(la*x3)*cos(la*x4)*cosh(lb*x3)*sin(lb*x4))*v4-
((cosh(la*x3)*cos(la*x4)*x1-sinh(la*x3)*sin(la*x4)*x2)*sinh(lb*x3)*cos(lb*x4)-
(sinh(la*x3)*sin(la*x4)*x1+cosh(la*x3)*cos(la*x4)*x2)*cosh(lb*x3)*sin(lb*x4)+(x1*sin
h(la*x3)*cos(la*x4)-x2*cosh(la*x3)*sin(la*x4))*cosh(lb*x3)*cos(lb*x4)-
(x2*sinh(la*x3)*cos(la*x4)+x1*cosh(la*x3)*sin(la*x4))*sinh(lb*x3)*sin(lb*x4))*i3+((sin
h(la*x3)*sin(la*x4)*x1+cosh(la*x3)*cos(la*x4)*x2)*sinh(lb*x3)*cos(lb*x4)+(cosh(la*x3
)*cos(la*x4)*x1-
sinh(la*x3)*sin(la*x4)*x2)*cosh(lb*x3)*sin(lb*x4)+(x2*sinh(la*x3)*cos(la*x4)+x1*cosh
(la*x3)*sin(la*x4))*cosh(lb*x3)*cos(lb*x4)+(x1*sinh(la*x3)*cos(la*x4)-
x2*cosh(la*x3)*sin(la*x4))*sinh(lb*x3)*sin(lb*x4))*i4-
(sinh(la*x3)*cos(la*x4)*sinh(lc*x3)*cos(lc*x4)-
cosh(la*x3)*sin(la*x4)*cosh(lc*x3)*sin(lc*x4))*v5+(cosh(la*x3)*sin(la*x4)*sinh(lc*x3)*
cos(lc*x4)+sinh(la*x3)*cos(la*x4)*cosh(lc*x3)*sin(lc*x4))*v6-
((x1*sinh(la*x3)*cos(la*x4)-x2*cosh(la*x3)*sin(la*x4))*cosh(lc*x3)*cos(lc*x4)-
(x2*sinh(la*x3)*cos(la*x4)+x1*cosh(la*x3)*sin(la*x4))*sinh(lc*x3)*sin(lc*x4))*i5+((x2
*sinh(la*x3)*cos(la*x4)+x1*cosh(la*x3)*sin(la*x4))*cosh(lc*x3)*cos(lc*x4)+(x1*sinh(la
*x3)*cos(la*x4)-x2*cosh(la*x3)*sin(la*x4))*sinh(lc*x3)*sin(lc*x4))*i6 =0
f2(x1,x2,x3,x4,x5) = imag(PT1) = 0
f2 = v2-
(sinh(la*x3)*sin(la*x4)*cosh(lb*x3)*cos(lb*x4)+cosh(la*x3)*cos(la*x4)*sinh(lb*x3)*sin(
lb*x4)+cosh(la*x3)*sin(la*x4)*sinh(lb*x3)*cos(lb*x4)+sinh(la*x3)*cos(la*x4)*cosh(lb*
x3)*sin(lb*x4))*v3-(cosh(la*x3)*cos(la*x4)*cosh(lb*x3)*cos(lb*x4)-
sinh(la*x3)*sin(la*x4)*sinh(lb*x3)*sin(lb*x4)+sinh(la*x3)*cos(la*x4)*sinh(lb*x3)*cos(l
b*x4)-cosh(la*x3)*sin(la*x4)*cosh(lb*x3)*sin(lb*x4))*v4-
((sinh(la*x3)*sin(la*x4)*x1+cosh(la*x3)*cos(la*x4)*x2)*sinh(lb*x3)*cos(lb*x4)+(cosh(l
a*x3)*cos(la*x4)*x1-
sinh(la*x3)*sin(la*x4)*x2)*cosh(lb*x3)*sin(lb*x4)+(x2*sinh(la*x3)*cos(la*x4)+x1*cosh
(la*x3)*sin(la*x4))*cosh(lb*x3)*cos(lb*x4)+(x1*sinh(la*x3)*cos(la*x4)-
x2*cosh(la*x3)*sin(la*x4))*sinh(lb*x3)*sin(lb*x4))*i3-((cosh(la*x3)*cos(la*x4)*x1-
sinh(la*x3)*sin(la*x4)*x2)*sinh(lb*x3)*cos(lb*x4)-
(sinh(la*x3)*sin(la*x4)*x1+cosh(la*x3)*cos(la*x4)*x2)*cosh(lb*x3)*sin(lb*x4)+(x1*sin
h(la*x3)*cos(la*x4)-x2*cosh(la*x3)*sin(la*x4))*cosh(lb*x3)*cos(lb*x4)-
(x2*sinh(la*x3)*cos(la*x4)+x1*cosh(la*x3)*sin(la*x4))*sinh(lb*x3)*sin(lb*x4))*i4-
(cosh(la*x3)*sin(la*x4)*sinh(lc*x3)*cos(lc*x4)+sinh(la*x3)*cos(la*x4)*cosh(lc*x3)*sin(
lc*x4))*v5-(sinh(la*x3)*cos(la*x4)*sinh(lc*x3)*cos(lc*x4)-
cosh(la*x3)*sin(la*x4)*cosh(lc*x3)*sin(lc*x4))*v6-
((x2*sinh(la*x3)*cos(la*x4)+x1*cosh(la*x3)*sin(la*x4))*cosh(lc*x3)*cos(lc*x4)+(x1*sin
h(la*x3)*cos(la*x4)-x2*cosh(la*x3)*sin(la*x4))*sinh(lc*x3)*sin(lc*x4))*i5-
126
((x1*sinh(la*x3)*cos(la*x4)-x2*cosh(la*x3)*sin(la*x4))*cosh(lc*x3)*cos(lc*x4)-
(x2*sinh(la*x3)*cos(la*x4)+x1*cosh(la*x3)*sin(la*x4))*sinh(lc*x3)*sin(lc*x4))*i6 =0
f3(x1,x2,x3,x4,x5) = real(PT2) = 0
f3= v3+(-
cosh(lb*x3)*cos(lb*x4)*cosh(lc*x3)*cos(lc*x4)+sinh(lb*x3)*sin(lb*x4)*sinh(lc*x3)*sin(l
c*x4)-
sinh(lb*x3)*cos(lb*x4)*sinh(lc*x3)*cos(lc*x4)+cosh(lb*x3)*sin(lb*x4)*cosh(lc*x3)*sin(l
c*x4))*v5-(-sinh(lb*x3)*sin(lb*x4)*cosh(lc*x3)*cos(lc*x4)-
cosh(lb*x3)*cos(lb*x4)*sinh(lc*x3)*sin(lc*x4)-
cosh(lb*x3)*sin(lb*x4)*sinh(lc*x3)*cos(lc*x4)-
sinh(lb*x3)*cos(lb*x4)*cosh(lc*x3)*sin(lc*x4))*v6+(-(cosh(lb*x3)*cos(lb*x4)*x1-
sinh(lb*x3)*sin(lb*x4)*x2)*sinh(lc*x3)*cos(lc*x4)+(sinh(lb*x3)*sin(lb*x4)*x1+cosh(lb*
x3)*cos(lb*x4)*x2)*cosh(lc*x3)*sin(lc*x4)-(x1*sinh(lb*x3)*cos(lb*x4)-
x2*cosh(lb*x3)*sin(lb*x4))*cosh(lc*x3)*cos(lc*x4)+(x2*sinh(lb*x3)*cos(lb*x4)+x1*cosh
(lb*x3)*sin(lb*x4))*sinh(lc*x3)*sin(lc*x4))*i5-(-
(sinh(lb*x3)*sin(lb*x4)*x1+cosh(lb*x3)*cos(lb*x4)*x2)*sinh(lc*x3)*cos(lc*x4)-
(cosh(lb*x3)*cos(lb*x4)*x1-sinh(lb*x3)*sin(lb*x4)*x2)*cosh(lc*x3)*sin(lc*x4)-
(x2*sinh(lb*x3)*cos(lb*x4)+x1*cosh(lb*x3)*sin(lb*x4))*cosh(lc*x3)*cos(lc*x4)-
(x1*sinh(lb*x3)*cos(lb*x4)-x2*cosh(lb*x3)*sin(lb*x4))*sinh(lc*x3)*sin(lc*x4))*i6+(-
sinh(la*x3)*cos(la*x4)*sinh(lb*x3)*cos(lb*x4)+cosh(la*x3)*sin(la*x4)*cosh(lb*x3)*sin(l
b*x4))*v1-(-sinh(la*x3)*cos(la*x4)*cosh(lb*x3)*sin(lb*x4)-
cosh(la*x3)*sin(la*x4)*sinh(lb*x3)*cos(lb*x4))*v2+((x1*sinh(lb*x3)*cos(lb*x4)-
x2*cosh(lb*x3)*sin(lb*x4))*cosh(la*x3)*cos(la*x4)-
(x2*sinh(lb*x3)*cos(lb*x4)+x1*cosh(lb*x3)*sin(lb*x4))*sinh(la*x3)*sin(la*x4))*i1-
((x2*sinh(lb*x3)*cos(lb*x4)+x1*cosh(lb*x3)*sin(lb*x4))*cosh(la*x3)*cos(la*x4)+(x1*si
nh(lb*x3)*cos(lb*x4)-x2*cosh(lb*x3)*sin(lb*x4))*sinh(la*x3)*sin(la*x4))*i2 =0
f4(x1,x2,x3,x4,x5) = imag(PT2) = 0
f4 = v4+(-sinh(lb*x3)*sin(lb*x4)*cosh(lc*x3)*cos(lc*x4)-
cosh(lb*x3)*cos(lb*x4)*sinh(lc*x3)*sin(lc*x4)-
cosh(lb*x3)*sin(lb*x4)*sinh(lc*x3)*cos(lc*x4)-
sinh(lb*x3)*cos(lb*x4)*cosh(lc*x3)*sin(lc*x4))*v5+(-
cosh(lb*x3)*cos(lb*x4)*cosh(lc*x3)*cos(lc*x4)+sinh(lb*x3)*sin(lb*x4)*sinh(lc*x3)*sin(l
c*x4)-
sinh(lb*x3)*cos(lb*x4)*sinh(lc*x3)*cos(lc*x4)+cosh(lb*x3)*sin(lb*x4)*cosh(lc*x3)*sin(l
c*x4))*v6+(-
(sinh(lb*x3)*sin(lb*x4)*x1+cosh(lb*x3)*cos(lb*x4)*x2)*sinh(lc*x3)*cos(lc*x4)-
(cosh(lb*x3)*cos(lb*x4)*x1-sinh(lb*x3)*sin(lb*x4)*x2)*cosh(lc*x3)*sin(lc*x4)-
(x2*sinh(lb*x3)*cos(lb*x4)+x1*cosh(lb*x3)*sin(lb*x4))*cosh(lc*x3)*cos(lc*x4)-
(x1*sinh(lb*x3)*cos(lb*x4)-x2*cosh(lb*x3)*sin(lb*x4))*sinh(lc*x3)*sin(lc*x4))*i5+(-
(cosh(lb*x3)*cos(lb*x4)*x1-
sinh(lb*x3)*sin(lb*x4)*x2)*sinh(lc*x3)*cos(lc*x4)+(sinh(lb*x3)*sin(lb*x4)*x1+cosh(lb*
x3)*cos(lb*x4)*x2)*cosh(lc*x3)*sin(lc*x4)-(x1*sinh(lb*x3)*cos(lb*x4)-
x2*cosh(lb*x3)*sin(lb*x4))*cosh(lc*x3)*cos(lc*x4)+(x2*sinh(lb*x3)*cos(lb*x4)+x1*cosh
(lb*x3)*sin(lb*x4))*sinh(lc*x3)*sin(lc*x4))*i6+(-
sinh(la*x3)*cos(la*x4)*cosh(lb*x3)*sin(lb*x4)-
cosh(la*x3)*sin(la*x4)*sinh(lb*x3)*cos(lb*x4))*v1+(-
127
sinh(la*x3)*cos(la*x4)*sinh(lb*x3)*cos(lb*x4)+cosh(la*x3)*sin(la*x4)*cosh(lb*x3)*sin(l
b*x4))*v2+((x2*sinh(lb*x3)*cos(lb*x4)+x1*cosh(lb*x3)*sin(lb*x4))*cosh(la*x3)*cos(la*
x4)+(x1*sinh(lb*x3)*cos(lb*x4)-
x2*cosh(lb*x3)*sin(lb*x4))*sinh(la*x3)*sin(la*x4))*i1+((x1*sinh(lb*x3)*cos(lb*x4)-
x2*cosh(lb*x3)*sin(lb*x4))*cosh(la*x3)*cos(la*x4)-
(x2*sinh(lb*x3)*cos(lb*x4)+x1*cosh(lb*x3)*sin(lb*x4))*sinh(la*x3)*sin(la*x4))*i2=0
f5(x1,x2,x3,x4,x5) = real(PT4) = 0
f5 = cosh(x5*x3)*cos(x5*x4)*v7-sinh(x5*x3)*sin(x5*x4)*v8+(-
sinh(x5*x3)*cos(x5*x4)*x1+cosh(x5*x3)*sin(x5*x4)*x2)*i7-(-
cosh(x5*x3)*sin(x5*x4)*x1-sinh(x5*x3)*cos(x5*x4)*x2)*i8+(-cosh(la*x3-
x3*x5)*cos(la*x4-x4*x5)*cosh(lb*x3)*cos(lb*x4)+sinh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*sinh(lb*x3)*sin(lb*x4)-sinh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*sinh(lb*x3)*cos(lb*x4)+cosh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*cosh(lb*x3)*sin(lb*x4))*v9-(-sinh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*cosh(lb*x3)*cos(lb*x4)-cosh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*sinh(lb*x3)*sin(lb*x4)-cosh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*sinh(lb*x3)*cos(lb*x4)-sinh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*cosh(lb*x3)*sin(lb*x4))*v10+((cosh(la*x3-x3*x5)*cos(la*x4-x4*x5)*x1-
sinh(la*x3-x3*x5)*sin(la*x4-x4*x5)*x2)*sinh(lb*x3)*cos(lb*x4)-(sinh(la*x3-
x3*x5)*sin(la*x4-x4*x5)*x1+cosh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*x2)*cosh(lb*x3)*sin(lb*x4)+(sinh(la*x3-x3*x5)*cos(la*x4-x4*x5)*x1-cosh(la*x3-
x3*x5)*sin(la*x4-x4*x5)*x2)*cosh(lb*x3)*cos(lb*x4)-(cosh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*x1+sinh(la*x3-x3*x5)*cos(la*x4-x4*x5)*x2)*sinh(lb*x3)*sin(lb*x4))*i9-
((sinh(la*x3-x3*x5)*sin(la*x4-x4*x5)*x1+cosh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*x2)*sinh(lb*x3)*cos(lb*x4)+(cosh(la*x3-x3*x5)*cos(la*x4-x4*x5)*x1-sinh(la*x3-
x3*x5)*sin(la*x4-x4*x5)*x2)*cosh(lb*x3)*sin(lb*x4)+(cosh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*x1+sinh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*x2)*cosh(lb*x3)*cos(lb*x4)+(sinh(la*x3-x3*x5)*cos(la*x4-x4*x5)*x1-
cosh(la*x3-x3*x5)*sin(la*x4-x4*x5)*x2)*sinh(lb*x3)*sin(lb*x4))*i10+(-sinh(la*x3-
x3*x5)*cos(la*x4-x4*x5)*sinh(lc*x3)*cos(lc*x4)+cosh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*cosh(lc*x3)*sin(lc*x4))*v11-(-cosh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*sinh(lc*x3)*cos(lc*x4)-sinh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*cosh(lc*x3)*sin(lc*x4))*v12+((sinh(la*x3-x3*x5)*cos(la*x4-x4*x5)*x1-
cosh(la*x3-x3*x5)*sin(la*x4-x4*x5)*x2)*cosh(lc*x3)*cos(lc*x4)-(cosh(la*x3-
x3*x5)*sin(la*x4-x4*x5)*x1+sinh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*x2)*sinh(lc*x3)*sin(lc*x4))*i11-((cosh(la*x3-x3*x5)*sin(la*x4-
x4*x5)*x1+sinh(la*x3-x3*x5)*cos(la*x4-
x4*x5)*x2)*cosh(lc*x3)*cos(lc*x4)+(sinh(la*x3-x3*x5)*cos(la*x4-x4*x5)*x1-cosh(la*x3-
x3*x5)*sin(la*x4-x4*x5)*x2)*sinh(lc*x3)*sin(lc*x4))*i12 =0
A.9. Phương trình (3.112)
f1, f2, f3, f4 tương tự như phụ lục A.9.
f5(x1,x2,x3,x4,x5) = real(PT4) = 0
128
f5 = cosh(x5*x3)*cos(x5*x4)*v9-sinh(x5*x3)*sin(x5*x4)*v10-
(sinh(x5*x3)*cos(x5*x4)*x1-
cosh(x5*x3)*sin(x5*x4)*x2)*i9+(cosh(x5*x3)*sin(x5*x4)*x1+sinh(x5*x3)*cos(x5*x4)*x2
)*i10-(cosh(lb*x3-x3*x5)*cos(lb*x4-x4*x5)*cosh(lc*x3)*cos(lc*x4)-sinh(lb*x3-
x3*x5)*sin(lb*x4-x4*x5)*sinh(lc*x3)*sin(lc*x4)+sinh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*sinh(lc*x3)*cos(lc*x4)-cosh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*cosh(lc*x3)*sin(lc*x4))*v11+(sinh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*cosh(lc*x3)*cos(lc*x4)+cosh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*sinh(lc*x3)*sin(lc*x4)+cosh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*sinh(lc*x3)*cos(lc*x4)+sinh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*cosh(lc*x3)*sin(lc*x4))*v12-(-(cosh(lb*x3-x3*x5)*cos(lb*x4-x4*x5)*x1-
sinh(lb*x3-x3*x5)*sin(lb*x4-x4*x5)*x2)*sinh(lc*x3)*cos(lc*x4)+(sinh(lb*x3-
x3*x5)*sin(lb*x4-x4*x5)*x1+cosh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*x2)*cosh(lc*x3)*sin(lc*x4)-(sinh(lb*x3-x3*x5)*cos(lb*x4-x4*x5)*x1-cosh(lb*x3-
x3*x5)*sin(lb*x4-x4*x5)*x2)*cosh(lc*x3)*cos(lc*x4)+(cosh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*x1+sinh(lb*x3-x3*x5)*cos(lb*x4-x4*x5)*x2)*sinh(lc*x3)*sin(lc*x4))*i11+(-
(sinh(lb*x3-x3*x5)*sin(lb*x4-x4*x5)*x1+cosh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*x2)*sinh(lc*x3)*cos(lc*x4)-(cosh(lb*x3-x3*x5)*cos(lb*x4-x4*x5)*x1-sinh(lb*x3-
x3*x5)*sin(lb*x4-x4*x5)*x2)*cosh(lc*x3)*sin(lc*x4)-(cosh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*x1+sinh(lb*x3-x3*x5)*cos(lb*x4-x4*x5)*x2)*cosh(lc*x3)*cos(lc*x4)-(sinh(lb*x3-
x3*x5)*cos(lb*x4-x4*x5)*x1-cosh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*x2)*sinh(lc*x3)*sin(lc*x4))*i12-(sinh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*sinh(la*x3)*cos(la*x4)-cosh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*cosh(la*x3)*sin(la*x4))*v7+(cosh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*sinh(la*x3)*cos(la*x4)+sinh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*cosh(la*x3)*sin(la*x4))*v8-((-sinh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*x1+cosh(lb*x3-x3*x5)*sin(lb*x4-x4*x5)*x2)*cosh(la*x3)*cos(la*x4)-(-
cosh(lb*x3-x3*x5)*sin(lb*x4-x4*x5)*x1-sinh(lb*x3-x3*x5)*cos(lb*x4-
x4*x5)*x2)*sinh(la*x3)*sin(la*x4))*i7+((-cosh(lb*x3-x3*x5)*sin(lb*x4-x4*x5)*x1-
sinh(lb*x3-x3*x5)*cos(lb*x4-x4*x5)*x2)*cosh(la*x3)*cos(la*x4)+(-sinh(lb*x3-
x3*x5)*cos(lb*x4-x4*x5)*x1+cosh(lb*x3-x3*x5)*sin(lb*x4-
x4*x5)*x2)*sinh(la*x3)*sin(la*x4))*i8=0
A.10. Phương trình (3.113)
f1, f2, f3, f4 tương tự như phụ lục A.9.
f5(x1,x2,x3,x4,x5) = real(PT4) = 0
f5 = cosh(x5*x3)*cos(x5*x4)*v11-sinh(x5*x3)*sin(x5*x4)*v12+(-
sinh(x5*x3)*cos(x5*x4)*x1+cosh(x5*x3)*sin(x5*x4)*x2)*i11-(-
cosh(x5*x3)*sin(x5*x4)*x1-sinh(x5*x3)*cos(x5*x4)*x2)*i12+(-
cosh(la*x3)*cos(la*x4)*cosh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)+sinh(la*x3)*sin(la*x4)*sinh(lc*x3-x3*x5)*sin(lc*x4-x4*x5)-sinh(lc*x3-
x3*x5)*cos(lc*x4-x4*x5)*sinh(la*x3)*cos(la*x4)+cosh(lc*x3-x3*x5)*sin(lc*x4-
x4*x5)*cosh(la*x3)*sin(la*x4))*v7-(-sinh(la*x3)*sin(la*x4)*cosh(lc*x3-
x3*x5)*cos(lc*x4-x4*x5)-cosh(la*x3)*cos(la*x4)*sinh(lc*x3-x3*x5)*sin(lc*x4-x4*x5)-
129
cosh(lc*x3-x3*x5)*sin(lc*x4-x4*x5)*sinh(la*x3)*cos(la*x4)-sinh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)*cosh(la*x3)*sin(la*x4))*v8+((cosh(lc*x3-x3*x5)*cos(lc*x4-x4*x5)*x1-
sinh(lc*x3-x3*x5)*sin(lc*x4-x4*x5)*x2)*sinh(la*x3)*cos(la*x4)-(sinh(lc*x3-
x3*x5)*sin(lc*x4-x4*x5)*x1+cosh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)*x2)*cosh(la*x3)*sin(la*x4)+(sinh(lc*x3-x3*x5)*cos(lc*x4-x4*x5)*x1-cosh(lc*x3-
x3*x5)*sin(lc*x4-x4*x5)*x2)*cosh(la*x3)*cos(la*x4)-(cosh(lc*x3-x3*x5)*sin(lc*x4-
x4*x5)*x1+sinh(lc*x3-x3*x5)*cos(lc*x4-x4*x5)*x2)*sinh(la*x3)*sin(la*x4))*i7-
((sinh(lc*x3-x3*x5)*sin(lc*x4-x4*x5)*x1+cosh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)*x2)*sinh(la*x3)*cos(la*x4)+(cosh(lc*x3-x3*x5)*cos(lc*x4-x4*x5)*x1-sinh(lc*x3-
x3*x5)*sin(lc*x4-x4*x5)*x2)*cosh(la*x3)*sin(la*x4)+(cosh(lc*x3-x3*x5)*sin(lc*x4-
x4*x5)*x1+sinh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)*x2)*cosh(la*x3)*cos(la*x4)+(sinh(lc*x3-x3*x5)*cos(lc*x4-x4*x5)*x1-cosh(lc*x3-
x3*x5)*sin(lc*x4-x4*x5)*x2)*sinh(la*x3)*sin(la*x4))*i8+(-sinh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)*sinh(lb*x3)*cos(lb*x4)+cosh(lc*x3-x3*x5)*sin(lc*x4-
x4*x5)*cosh(lb*x3)*sin(lb*x4))*v9-(-cosh(lc*x3-x3*x5)*sin(lc*x4-
x4*x5)*sinh(lb*x3)*cos(lb*x4)-sinh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)*cosh(lb*x3)*sin(lb*x4))*v10+((sinh(lc*x3-x3*x5)*cos(lc*x4-x4*x5)*x1-
cosh(lc*x3-x3*x5)*sin(lc*x4-x4*x5)*x2)*cosh(lb*x3)*cos(lb*x4)-(cosh(lc*x3-
x3*x5)*sin(lc*x4-x4*x5)*x1+sinh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)*x2)*sinh(lb*x3)*sin(lb*x4))*i9-((cosh(lc*x3-x3*x5)*sin(lc*x4-
x4*x5)*x1+sinh(lc*x3-x3*x5)*cos(lc*x4-
x4*x5)*x2)*cosh(lb*x3)*cos(lb*x4)+(sinh(lc*x3-x3*x5)*cos(lc*x4-x4*x5)*x1-cosh(lc*x3-
x3*x5)*sin(lc*x4-x4*x5)*x2)*sinh(lb*x3)*sin(lb*x4))*i10=0
Các file đính kèm theo tài liệu này:
luan_an_nghien_cuu_phuong_phap_xac_dinh_vi_tri_su_co_tren_du.pdf
