Variational procedure and generalized Lanczos recursion for small-amplitude classical oscillations

TL;DR

This paper introduces a variational method to compute the lowest frequencies of small-amplitude oscillations in classical Hamiltonian systems and generalizes the Lanczos recursion to handle associated non-Hermitian eigenvalue problems.

Contribution

It presents a novel variational approach combined with a generalized Lanczos recursion for non-Hermitian eigenproblems in classical oscillation analysis.

Findings

Effective computation of lowest oscillation frequencies

Generalization of Lanczos recursion to non-Hermitian cases

Potential applications in classical mechanics analysis

Abstract

Variational procedure is developed that yields lowest frequencies of small-amplitude oscillations of classical Hamiltonian systems. Genuine Lanczos recursion is generalized to treat related non-Hermitian eigenvalue problems.