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О причинах расхождения результатов расчета и эксперимента…
Инженерный журнал: наука и инновации
# 2·2017 15
On the causes of divergence of calculation results and
experiment when determining stability boundaries
for the inverted pendulums
(by the article of D.J. Acheson and T. Mullin in
Nature
)
© V.A. Gribkov, Ya.D. Gordin
Bauman Moscow State Technical University, Moscow, Russia
The article analyses the results published by D.J. Acheson, T. Mullin in the journal “Na-
ture”. The famous article covered the experimental and calculated determination of the
stability boundaries for single, double and triple inverted pendulums vibration stabilized.
It marked a radical discrepancy between the results of calculations and experiments to
double and triple pendulums (lack of coordination between the calculated and experi-
mental boundaries of the stability boundaries). The aim of the paper is to find the causes
that led to a significant difference in the position of the calculated and experimental sta-
bility boundaries of double and triple inverted pendulum, as well as checking the opera-
bility and effectiveness of D.J. Acheson pendulum theorem.
Checking calculation of the boundaries of sustainability was not possible due to lack of
some parameters required for solving the problem of pendulum systems. Through the pa-
rameters given in the article, using the range of sizes in the core tubular elements pendu-
lums, with the help of numerical experiments in SOLIDWORKS we restored the missing
dimensions and inertial characteristics. D.J. Acheson pendulum theorem, using natural
frequencies of direct pendulums we received updated stability region. For double and
triple pendulums we specified range of the stability region closer to the experimental in a
significant range of the excitation parameters. Thus we confirmed performance of
D.J. Acheson pendulum theorem. It is proved that the radical divergence between the
calculated and experimental boundaries of sustainability in the article by D.J. Acheson
and T. Mullin caused a large error in determining the higher natural vibration frequen-
cies of double and triple pendulums (all own frequencies were determined experimentally
using the main parametric resonance of pendulums).
Keywords:
inverted physical pendulum, N-linked pendulum, parametric excitation, dy-
namic stability, experiment
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