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Restrictions of Quadratic Forms to Lagrangian Planes, Quadratic Matrix Equations, and Gyroscopic Stabilization

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Abstract

We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are determined by the solutions of quadratic matrix equations of a special form. New conditions for gyroscopic stabilization are found.

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References

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Authors and Affiliations

  1. V. A. Steklov Institute of Mathematics, Russia

    V. V. Kozlov

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  1. V. V. Kozlov
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__________

Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 39, No. 4, pp. 32–47, 2005

Original Russian Text Copyright © by V. V. Kozlov

This research was performed in the framework of the Program “State Support for Leading Scientific Schools” (grant No. NSh-136.2003.1).

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Kozlov, V.V. Restrictions of Quadratic Forms to Lagrangian Planes, Quadratic Matrix Equations, and Gyroscopic Stabilization. Funct Anal Its Appl 39, 271–283 (2005). https://doi.org/10.1007/s10688-005-0048-y

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  • DOI: https://doi.org/10.1007/s10688-005-0048-y

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