Modeling of multistage pendulums: Triple pendulum suspension for GEO 600

2000 ◽  
Vol 71 (6) ◽  
pp. 2546-2551 ◽  
Author(s):  
M. E. Husman ◽  
C. I. Torrie ◽  
M. V. Plissi ◽  
N. A. Robertson ◽  
K. A. Strain ◽  
...  
Keyword(s):  
Triple Pendulum ◽  
Pendulum Suspension

scholarly journals GEO 600 triple pendulum suspension system: Seismic isolation and control

2000 ◽  
Vol 71 (6) ◽  
pp. 2539-2545 ◽  
Author(s):  
M. V. Plissi ◽  
C. I. Torrie ◽  
M. E. Husman ◽  
N. A. Robertson ◽  
K. A. Strain ◽  
...  
Keyword(s):  
Seismic Isolation ◽  
Suspension System ◽  
Triple Pendulum ◽  
And Control ◽  
Pendulum Suspension

EXPERIMENTAL STUDY OF CHAOS IN A DRIVEN TRIPLE PENDULUM

1999 ◽  
Vol 227 (1) ◽  
pp. 230-238 ◽  
Author(s):  
Q. ZHU ◽  
M. ISHITOBI
Keyword(s):  
Experimental Study ◽  
Triple Pendulum

Forced Oscillations for the Triple Pendulum

1990 ◽  
pp. 177-208 ◽  
Author(s):  
Kung-Ching Chang ◽  
Yiming Long ◽  
Eduard Zehnder
Keyword(s):  
Forced Oscillations ◽  
Triple Pendulum

A new pendulum suspension

1880 ◽  
Vol 110 (1) ◽  
pp. 47-48
Author(s):  
Louis H. Spellier
Keyword(s):  
Pendulum Suspension

Stability Analysis of Parametrically Excited Systems Using the Energy-Growth Exponent/Coefficient

2017 ◽  
Vol 17 (02) ◽  
pp. 1750018 ◽  
Author(s):  
Yuchun Li ◽  
Lishi Wang ◽  
Yanqing Yu
Keyword(s):  
Parametric Instability ◽  
Mathieu Equation ◽  
Energy Criterion ◽  
Growth Exponent ◽  
Parametrically Excited ◽  
Floquet Exponent ◽  
Energy Growth ◽  
Triple Pendulum ◽  
Analytical Formulae ◽  
The Stability

In this paper, the energy exponent is used to study the instability of parametrically excited systems governed by the damped Mathieu equation. Through the numerical tests, an energy-growth exponent (EGE) is adopted to evaluate the instability intensity and instability boundary of the system. The EGE can be expressed as a product of the modal frequency and a dimensionless coefficient, defined as the energy-growth coefficient (EGC). Based on the Floquet theory, the relationship between the EGE, Floquet exponent and Lyapunov exponent are derived. An energy criterion of parametric instability is proposed by using the EGE. Using a simple pendulum as an example, the geometric characteristics of the EGC are investigated, and approximate analytical formulae of the EGC/EGE for three different unstable patterns are developed. The EGC/EGE formulae are applicable to the parametrically excited systems governed by the damped Mathieu equation. The unstable behaviors and properties of parametric vibrations are analyzed and discussed in details with EGE/EGC for three systems including a triple pendulum, two-dimensional sloshing fluid, and a two-span continuous beam. The stability boundaries established by using EGE/EGC agree well with those by the conventional theory and experiment. As a practical tool, the EGE/EGC formulae can be easily applied to analyzing the unstable intensities and boundaries of the parametrically excited systems.

Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum

Open Physics ◽  
2014 ◽  
Vol 12 (8) ◽  
Author(s):  
Raoul Nigmatullin ◽  
Sergey Osokin ◽  
Jan Awrejcewicz ◽  
Grzegorz Kudra
Keyword(s):  
Chaotic Behavior ◽  
Quantitative Description ◽  
Pendulum System ◽  
Scaling Properties ◽  
Fourier Decomposition ◽  
Random Functions ◽  
Periodic Processes ◽  
Triple Pendulum ◽  
Random Behavior ◽  
Invariant Properties

AbstractIn this paper we apply a new method of analysis of random behavior of chaotic systems based on the Prony decomposition. The generalized Prony spectrum (GPS) is used for quantitative description of a wide class of random functions when information about their probability distribution function is absent. The scaling properties of the random functions that keep their invariant properties on some range of scales help to fit the compressed function based on the Prony’s decomposition. In paper [1] the first author (RRN) found the physical interpretation of this decomposition that includes the conventional Fourier decomposition as a partial case. It has been proved also that the GPS can be used for detection of quasi-periodic processes that are appeared usually in the repeated or similar measurements. A triple physical pendulum is used as a chaotic system to obtain a chaotic behavior of displacement angles with one, two and three positive Lyapunov’s exponents (LEs). The chaotic behavior of these angles can be expressed in the form of amplitude-frequency response (AFR) that is extracted from the corresponding GPS and can serve as a specific ”fingerprint” characterizing the random behavior of the triple-pendulum system studied. This new quantitative presentation of random data opens additional possibilities in classification of chaotic responses and random behaviors of different complex systems.

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