Eigenvalue Problem for Lagrangian Systems. IV

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Abstract
The constants of the motion of the linear Lagrangian system ξ¨+Aξ̇+Hξ(t)=0 are shown to generate a useful class of orthogonality relations. For systems with complete sets of eigenvectors, these are used to derive the expansion coefficients for arbitrary initial data. We show that every stable system possesses a complete set of eigenvectors and that this set is the union of two basis sets.

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