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Linear systems with a quadratic integral and symplectic geometry of artin spaces

✍ Scribed by V.V. Kozlov

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
770 KB
Volume
68
Category
Article
ISSN
0021-8928

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✦ Synopsis

New relations are established between the spectrum of a linear system and the indices of inertia of its quadratic integral. A detailed investigation is made of the case in which the positive and negative indices of inertia of the quadratic integral are identical. Conditions are found under which the singular planes will be Lagrangian relative to some natural symplectic structure. They are closely related to the conditions for strong stability of a linear system. The general results are applied to the classical problem of gyroscopic stabilization.

πŸ“œ SIMILAR VOLUMES

NORMAL MODE LOCALIZATION FOR A TWO DEGRE
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✍ R. BHATTACHARYYA; P. JAIN; A. NAIR πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 249 KB

The non-similar normal modes of free oscillations of a coupled non-linear oscillator are examined. So far, the study of non-linear vibrations has been based on the assumption that the system is admissible. This requirement is satis"ed when the sti!ness of the springs are odd functions of their displ