Eigenvalue Problem for Lagrangian Systems

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Abstract
The problem of small oscillations about a state of steady motion of a Lagrangian system is considered. Upper and lower bounds for the growth rates of unstable systems are obtained; sufficient conditions for instability are given for finite dimensional systems; an existence theorem for stable modes for systems with an infinite number of degrees of freedom is presented (valid when the operators are completely continuous in Hilbert space); and finally the orthogonality and completeness properties of the modes of stable finite dimensional systems are discussed.