Lambda-matrices and Vibrating SystemsCourier Corporation, 1 janv. 2002 - 193 pages Features aspects and solutions of problems of linear vibrating systems with a finite number of degrees of freedom. Starts with development of necessary tools in matrix theory, followed by numerical procedures for relevant matrix formulations and relevant theory of differential equations. Minimum of mathematical abstraction; assumes a familiarity with matrix theory, elementary calculus. 1966 edition. |
Table des matières
A SKETCH OF SOME MATRIX THEORY | 1 |
REGULAR PENCILS OF MATRICES AND EIGENVALUE PROBLEMS | 23 |
LAMBDAMATRICES I | 42 |
LAMBDAMATRICES II | 56 |
SOME NUMERICAL METHODS FOR LAMBDAMATRICES | 75 |
ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS | 100 |
THE THEORY OF VIBRATING SYSTEMS | 116 |
ON THE THEORY OF RESONANCE TESTING | 143 |
FURTHER RESULTS FOR SYSTEMS WITH DAMPING | 158 |
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Expressions et termes fréquents
A₁ algorithm analysis applied associated assume Chapter coefficients coincide columns compute consider constant corresponding damped system deduce defined denote derivatives diag diagonal matrix differential equations eigen elementary divisors elements eqns exist finite functions Gantmacher gives hence hysteretic implies inverse iteration LAMBDA-MATRICES latent roots left eigenvectors left latent vectors lemma linear combination linearly independent linearly independent right method multiplicity natural frequencies non-negative definite non-singular matrix non-zero null eigenvalue obtain orthogonal partitions pencil of matrices perturbation polynomial positive definite premultiply problem proof proper numbers properties q'Aq rate of convergence Rayleigh quotient Real Imaginary real symmetric regular pencil right and left right eigenvectors right latent vectors satisfied scalar simple 2-matrix simple matrix pencil simple pencil simple structure solution square matrix subspaces of right symmetric matrix Theorem 2.5 theory transformation undamped natural frequencies vector space vectors q write zero