TY - JOUR
A2 - Cleaver, G.
AU - Stanovnik, Aleš
AU - Jurcic-Zlobec, Borut
PY - 2012
DA - 2012/01/15
TI - Numerical Study of the Elastic Pendulum on the Rotating Earth
SP - 806231
VL - 2012
AB - The elastic pendulum is a simple physical system represented by nonlinear differential equations. Analytical solutions for the bob trajectories on the rotating earth may be obtained in two limiting cases: for the ideally elastic pendulum with zero unstressed string length and for the Foucault pendulum with an inextensible string. The precession period of the oscillation plane, as seen by the local observer on the rotating earth, is 24 hours in the first case and has a well-known latitude dependence in the second case. In the present work, we have obtained numerical solutions of the nonlinear equations for different string elasticities in order to study the transition from one precession period to the other. It is found that the transition is abrupt and that it occurs for a quite small perturbation of the ideally elastic pendulum, that is, for the unstressed string length equal to about 10^{−4} of the equilibrium length due to theweight of the bob.
SN - xxxx-xxxx
UR - https://doi.org/10.5402/2012/806231
DO - 10.5402/2012/806231
JF - ISRN Mathematical Physics
PB - International Scholarly Research Network
KW -
ER -