14. starptautiskā konference 2012 - Latvijas Jūras akadēmija

Proceedings of 14th International conference „Maritime Transport and Infrastructure - 2012”In order to ensure that function (18) satisfies non – homogenous equation the system[3],[4]:must be sated for solving alternating constants:C1C1ty1tC2ty2t 0;tytCtyt f t.122(19)The homogenous differential equation (3) has particular solutions:yt t;y t sint1cos2 (20)Functions (20) should be inserted in system (19). The system is acquired:C1 Ctcos t C 2tsint 0; tsin t Ctcos t f t.12(21)By solving system (16), acquired:By integrating calculate:1 t f t sin; C t f t costC1 t 12. (22)C11t f t sind C ;11C2t f tcosd C2. (23)The frontiers of integrals are chosen in accordance with terms in the beginning. Theexpressions of constants (23) and particular solutions (22) must be inserted in formula (18): 1y C1 cost C2sint f td sin. (24)The integral:ttf t f ftd f t f tf1 2121 2d(25)0is called convolution or composition of function. Linear differential equation with constantcoefficients of third grade.After solving system [1, III50], of differential equations of movement of gyrocompass a thirdgrade differential equation with constant coefficients is acquired which describes the movement ofgyrocompass which is dependent from azimuth:0 ya y a y a y f . (26) 1 2 3Here coefficients a1 , a2,a3and free member f includes parameters of the device. The solutionof equation is stated with sum (2) where y is general solution of appropriate homogenous differentialequation:82