Application of Hamilton's principle to the study of the anharmonic oscillator in classical mechanics

Journal Article · Sun Jul 01 04:00:00 EDT 1979 · Am. J. Phys.; (United States)

DOI:https://doi.org/10.1119/1.11948· OSTI ID:5985400

Gilmartin, H; Klein, A; Li, C

A form of Hamilton's principle for classical mechanics, appropriate to the study of arbitrary self-sustained vibrations in one dimension is presented. It is applied as an approximate computational tool to the study of several examples of anharmonic oscillation. The trial function is a finite Fourier series chosen to approach the exact solution as the number of terms increases without limit. Analytic approximations can be obtained for the limits of weak and strong anharmonicity. Numerical results for the amplitude-dependent frequencies compare favorably with the exact solutions.

• Research Organization: Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania, 19104
• OSTI ID: 5985400
• Report Number(s): CONF-781095-
• Journal Information: Am. J. Phys.; (United States), Journal Name: Am. J. Phys.; (United States) Vol. 47:7; ISSN AJPIA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
ELECTRONIC EQUIPMENT
FOURIER ANALYSIS
HAMILTONIANS
HARMONICS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
NUMERICAL ANALYSIS
OSCILLATION MODES
OSCILLATIONS
OSCILLATORS
PERTURBATION THEORY
QUANTUM OPERATORS
VARIATIONAL METHODS