Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975a%26a....40..147h&link_type=abstract
Astronomy and Astrophysics, vol. 40, no. 1-2, Apr. 1975, p. 147-159.
Astronomy and Astrophysics
Astrophysics
9
Motion Stability, Orbital Mechanics, Pendulums, Periodic Functions, Springs (Elastic), Vibration Mode, Asymptotic Methods, Computer Techniques, Degrees Of Freedom, Equations Of Motion, Gravitational Effects, Resonant Vibration, Stable Oscillations, X-Y Plotters
Scientific paper
A simple dynamics problem of two degrees of freedom is investigated numerically for the case of a planar spring-pendulum configuration consisting of a mass attached to a linear spring inserted in a constant gravity field. Methods from orbit theory are used to obtain symmetric periodic orbits and evaluate their stability, eleven families of periodic solutions are identified, and their evolution relative to the energy constant is determined. Characteristics of the families are given for three values of a free parameter, and the stability index is evaluated along each family for the particular value of this parameter which corresponds to the lowest-order resonance between the spring and pendulum modes of oscillation. Various families are found to be simple-periodic, double-periodic, or triple-periodic, and numerous bifurcations are noted.
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