scholarly journals Mathematical Modelling and Analysis of Human Arm as a Triple Pendulum System using Euler – Lagragian Model

Author(s):  
Michael C. Agarana ◽  
Esther T. Akinlabi
Open Physics ◽  
2014 ◽  
Vol 12 (8) ◽  
Author(s):  
Raoul Nigmatullin ◽  
Sergey Osokin ◽  
Jan Awrejcewicz ◽  
Grzegorz Kudra

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.


2021 ◽  
Vol 48 (4) ◽  
Author(s):  
T. S. Amer ◽  
◽  
A. A. Galal ◽  
A. F. Abolila ◽  
◽  
...  

In this article, a nonlinear dynamical system with three degrees of freedom (DOF) consisting of multiple pendulums (MP) is investigated. The motion of this system is restricted to be in a vertical plane, in which its pivot point moves in a circular path with constant angular velocity, under the action of an external harmonic force and a moment acting perpendicular to the direction of the last arm of MP and at the suspension point respectively. Multiple scales technique (MST) among other perturbation methods is used to obtain the approximate solutions of the equations of motion up to the third approximation because it is authorizing to execute a specific analysis of the system behaviour and to realize the solvability conditions given the resonance cases. The stability of the considered dynamical model utilizing the nonlinear stability analysis approach is examined. The solutions diagrams and resonance curves are drawn to illustrate the extent of the effect of various parameters on the solutions. The importance of this work is due to its uses in human or robotic walking analysis.


2021 ◽  
Author(s):  
Bikram Paul

<div>Recent advancements in the domain of quantum computing are posing a security threat to the classical cryptography algorithms. Popular symmetric and asymmetric cryptosystems including RSA, ECC, DES, Diffie-Hellman etc. can be broken by a quantum computer executing Shors and Grovers algorithms. This motivated scientific community to design newer encryption schemes to address security vulnerabilities. Hash, Code, Lattice, Multivariate Polynomial based cryptography algorithms, known as post-quantum cryptography algorithms (PQC), exhibit resistance against classical as well as quantum crypto-attacks. Apart from these PQC algorithms, a relatively new method of constructing cryptosystems utilizing the unpredictability property of discrete chaotic dynamic systems has become noteworthy from the practical perspective. In this paper, we present a novel approach to design an encryption scheme based on the chaotic dynamic physical system, which is derived from a mechanical model depicting nonlinear dynamics and exhibits resistance against various attacks. The effectiveness of the proposed cryptography scheme is validated against various standard tests, such as Lyapunov exponents test, bifurcation diagrams, sensitivity to parametric and to initial values, ergodicity, collision test, NIST, diehard randomness test etc. This algorithm is also verified through an FPGA implementation to assess its usage in low power high throughput applications as well. The power consumption and resource utilization of the proposed design are 56 % and 72.6 %, respectively, as compared to other known methods while operating at 628.14 MHz. It is observed that the proposed design can work efficiently with various wide range of applications. It is observed that the proposed design can work efficiently with various wide range of applications. The average power and area of its ASIC implementation at 180 nm technology are 61.8836 mW and 0.20374 mm 2 at 250 MHz, respectively.</div>


2021 ◽  
Author(s):  
Bikram Paul

<div>Recent advancements in the domain of quantum computing are posing a security threat to the classical cryptography algorithms. Popular symmetric and asymmetric cryptosystems including RSA, ECC, DES, Diffie-Hellman etc. can be broken by a quantum computer executing Shors and Grovers algorithms. This motivated scientific community to design newer encryption schemes to address security vulnerabilities. Hash, Code, Lattice, Multivariate Polynomial based cryptography algorithms, known as post-quantum cryptography algorithms (PQC), exhibit resistance against classical as well as quantum crypto-attacks. Apart from these PQC algorithms, a relatively new method of constructing cryptosystems utilizing the unpredictability property of discrete chaotic dynamic systems has become noteworthy from the practical perspective. In this paper, we present a novel approach to design an encryption scheme based on the chaotic dynamic physical system, which is derived from a mechanical model depicting nonlinear dynamics and exhibits resistance against various attacks. The effectiveness of the proposed cryptography scheme is validated against various standard tests, such as Lyapunov exponents test, bifurcation diagrams, sensitivity to parametric and to initial values, ergodicity, collision test, NIST, diehard randomness test etc. This algorithm is also verified through an FPGA implementation to assess its usage in low power high throughput applications as well. The power consumption and resource utilization of the proposed design are 56 % and 72.6 %, respectively, as compared to other known methods while operating at 628.14 MHz. It is observed that the proposed design can work efficiently with various wide range of applications. It is observed that the proposed design can work efficiently with various wide range of applications. The average power and area of its ASIC implementation at 180 nm technology are 61.8836 mW and 0.20374 mm 2 at 250 MHz, respectively.</div>


2012 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Natalja Kosareva ◽  
Olga Navickiene

Pneumologie ◽  
2017 ◽  
Vol 71 (S 01) ◽  
pp. S1-S125
Author(s):  
S Berger ◽  
C Gökeri ◽  
U Behrendt ◽  
SM Wienhold ◽  
J Lienau ◽  
...  

2003 ◽  
Author(s):  
Qi-Xiao Ye ◽  
Werner Blum ◽  
Ken Houston ◽  
Qi-Yuan Jiang

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