Issue 45

O. Reut et alii, Frattura ed Integrità Strutturale, 45 (2018) 183-190; DOI: 10.3221/IGF-ESIS.45.16 185         2 2 2 ' , ' , , 0 n n n n r r r r q r              2 2 2 sin , , sin sin n n n r n r                 (4) A change of variables x r q  was done in the Eqn. (4). It was rewritten with the new variables in the following form 2 2 ' , ' , , 0 n n n n x x x x x q q q                                    (5) The Kantorovich-Lebedev integral transformation with regard to variable x is applied to the equality (5)     0 , i n n K x x dx q x                (6) In the transformations (6) domain the Eqn. (5) can be reformulated as     2 1 0 4 n n n                  (7) There is no possibility to apply the integral Legendre transformation by the usual scheme to the Eqn. (7) because there are discontinuities of the function   n    and its derivative when    . The jumps have the following form 0 0 , , , 0, , 0, , , , , , , x x x q q q x x q q x q                                                                          (8) The integral Legendre’s transformation is applied to the Eqn. (7) by the generalized scheme [15]     0 cos sin n n k n k P d            (9) It leads to the linear algebraic equation in the transformations (3), (6), (9) domain             2 2 cos 1 / 2 sin cos n n k n k n k n dP k P d                              We will accept the designation     cos cos n n k k dP dP d d         in future. Here