On the stability of linear continuous systems. (English) Zbl 0151.36103
Keywords:
mechanics of solidsReferences:
| [1] | A. Liapounoff,Problème général de la stabilité du mouvement, Princeton: Princeton Univ. Press (1947). · Zbl 0031.18403 |
| [2] | H. Ziegler,Linear Elastic Stability, J. Appl. Math. Phys. (ZAMP)4, 1–50 (1953). · Zbl 0050.23905 · doi:10.1007/BF02075302 |
| [3] | W. T. Koiter,Over de stabiliteit van het elastisch eveniwicht, Thesis, Delft, Amsterdam: H. J. Paris (1945). |
| [4] | R. T. Shield andA. E. Green,On Certain Methods in the Stability Theory of Continuous Systems, Arch. Rational Mech. Anal.12, 354–360 (1963). · Zbl 0112.39003 · doi:10.1007/BF00281232 |
| [5] | E. Hellinger,Die allgemeinen Ansätze der Mechanik der Kontinua, Encyklopädie der Mathematischen Wissenschaften, Band IV4, 602–685, Leipzig Teubner (1914). |
| [6] | R. Courant,Partial Differential Equations (vol. 2 of Methods of Mathematical Physics by R. Courant and D. Hilbert), New York: Interscience (1962). · Zbl 0099.29504 |
| [7] | A. M. Slobodkin,On the Stability of the Equilibrium of Conservative Systems with an Infinite Number of Degrees of Freedom, Appl. Math. Mech. (Prikl. Mat. Mekh.)26, 356–358 (1962). · Zbl 0104.31003 |
| [8] | E. L. Ince,Ordinary Differential Equations, New York: Dover (1956). · Zbl 0063.02971 |
| [9] | A. A. Movchan,The Direct Method of Liapunov in Stability Problems of Elastic Systems, Appl. Math. Mech. (Prikl. Mat. Mekh.)23, 483–493 (1959). |
| [10] | O. D. Kellogg,Foundations of Potential Theory, New York: Dover (1953). · Zbl 0053.07301 |
| [11] | A. E. Green andW. Zerna,Theoretical Elasticity, Oxford: Oxford Univ. Press (1954). |
| [12] | R. L. Fosdick andR. T. Shield,Extremum Principles in the Theory of Small Elastic Deformations Superposed on Large Elastic Deformations, Progress in Applied Mechanics, 107–125, New York: Macmillan (1963). |
| [13] | C. B. Morrey, Jr.,Second Order Elliptic Systems of Differential Equations, Annals Math. Studies33, 101–159 (1954). · Zbl 0057.08301 |
| [14] | I. Fredholm,Sur les équations de l’équilibre d’un corps solide élastique, Acta Math.23, 1–42 (1900). · JFM 30.0715.02 · doi:10.1007/BF02418668 |
| [15] | T. C. Woo andR. T. Shield,Fundamental Solutions for Small Deformations Superposed on Finite Biaxial Extension of an Elastic Body, Arch. Rational Mech. Anal.9, 196–224 (1962). · Zbl 0109.42603 · doi:10.1007/BF00253345 |
| [16] | H. Zorski,On the Equations Describing Small Deformations Superposed on Finite Deformation, Proc. Inter. Symp. on Second-Order Effects in Elasticity, Plasticity and Fluid Dynamics, Haifa, 1962, Oxford, Pergamon Press (1964). · Zbl 0139.18502 |
| [17] | L. van Hove,Sur l’extension de la condition de Legendre du calcul des variations aux intégrals multiples à plusieurs fonctions inconnues, Konink. Nederl. Akad. Wetensch.50, 18–23 (1947). · Zbl 0029.26802 |
| [18] | J. Hadamard,Leçons sur la propagation des ondes et les equations de l’hydrodynamique, New York: Chelsea (1949). |
| [19] | J. L. Ericksen andR. A. Toupin,Implications of Hadamard’s Condition for Elastic Stability with Respect to Uniqueness Theorems, Canadian J. Math.8, 432–436 (1956). · Zbl 0071.39801 · doi:10.4153/CJM-1956-051-2 |
| [20] | R. Hill,On Uniqueness and Stability in the Theory of Finite Elastic Strain, J. Mech. Phys. Solids5, 229–241 (1957). · Zbl 0080.18004 · doi:10.1016/0022-5096(57)90016-9 |
| [21] | R. Courant andD. Hilbert,Methods of Mathematical Physics, Volume I, New York: Interscience (1953). · Zbl 0051.28802 |
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