Время науки - The Times of Science

Время науки The Times of Science 8 №4 5 = − + 1 , 6 = − 1 , 7 = − 1 , 8 = − + 1 , (17) where = √ √ 3 2 + 3 2 + 3 2 , 1 = 3 √ √ 3 2 + 3 2 − 3 2 , = √ √ 3 ′ 2 + 3 ′ 2 + 3 ′ 2 , 1 = 3 ′ √ √ 3 ′ 2 + 3 ′ 2 − 3 ′ 2 , (18) Here for 3 , 3 , 3 ′ , 3 ′ we have the values: 3 = 2 2( 2 +1) , 3 = 2 2( 2 +1) , 3 ′ = 2 ′ 2( 2 +1) , 3 ′ = 2 ′ 2( 2 +1) , (19) and 2 = − 2 + √ √ 1 2 + 1 2 + 1 2 , 2 = 2 + 1 √ √ 1 2 + 1 2 − 1 2 , 2 ′ = − 2 − √ √ 1 2 + 1 2 + 1 2 , 2 ′ = 2 − 1 √ √ 1 2 + 1 2 − 1 2 , (20) The values of 1 and 1 will be: 1 = 4 2 + 4 2 2 + 2 2 − 2 2 2 − 4 − 4 3 , 1 = −4 2 − 4 2 3 − 2 2 2 − 4 − 4 2 . (21) Here 1 , 2 , 3 , 4 are the roots of the first equation from (16), and 5 , 6 , 7 , 8 are the roots of the second equation. The roots 1 and 5 , 2 and 6 , 3 and 8 , 4 and 7 are complex conjugates. Thus, using the inverse Laplace transform of the elementary transforms, we obtain the values of the functions ( ) and ( ) in the following form: 1 ( ) = − (2 1 cos 1 + 2 1 sin 1 ) + (2 2 cos 1 − 2 2 sin 1 ) + − (2 3 cos 1 + 2 3 sin 1 ) + (2 4 cos 1 − 2 4 sin 1 ) 1 ( ) = − (2 1 ′ cos 1 + 2 1 ′ sin 1 ) + (2 2 ′ cos 1 − 2 2 ′ sin 1 )