In this proposed paper, based on the dynamic equation of linear gyroscopic system,the differential equation in Lagrange system is transformed into Hamilton system, and then the weighted adjoint symplectic orthogonal relations between the eigenvectors and the expansion theorem for arbitrary state vector are given in state space. Based on the above relations, the equations for modal perturbation analysis and the sensibility computation of eigenvectors are established, and a new effective algorithm for modal perturbation analysis and the sensibility computation is proposed, which can eliminate the traditional difficulties in perturbation analysis and sensibility computation in Lagrange system. An example shows the effectiveness of the numerical method of this paper.