Eigenvalue and Eigenvector Problems in Applied Mechanics
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Beschreibung
This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications.
This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications.
Presents several problems of applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors Studies mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems Explores a wealth of engineering applications
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Themen in »Eigenvalue and Eigenvector Problems in Applied Mechanics«
Eigenvalues Matrix analysis Continuum mechanics Mechanical Vibration Elastic stability Dynamic stability Rigid Body Dynamics Quadratic Forms Strain and Stress Tensor matrix theory
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“The book can serve as an introductory text for anybody interested in determining of eigenvalues and eigenvectors of mechanical systems, as well as frequencies and forms of free vibrations. Graduate students and researchers in mechanical and computational engineering will also find this book very useful.” (V. Leontiev, zbMATH 1407.74002, 2019)
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