Analysis of chaotic characteristics of trigonometric function system

2020 ◽  
Vol 34 (21) ◽  
pp. 2050210
Author(s):  
Wanbo Yu ◽  
Ting Yu
Keyword(s):  
Social Sciences ◽  
Dynamic System ◽  
Necessary Conditions ◽  
Fluid Motion ◽  
Nonlinear Dynamic System ◽  
Chaotic Sequence ◽  
Trigonometric System ◽  
Secure Communications ◽  
Key Space ◽  
Mathematical Derivation

Chaos, as an important subject of nonlinear science, plays an important role in solving problems in both natural sciences and social sciences such as the fields of secure communications, fluid motion, particle motion and so on. Aiming at this problem, this paper proposes a nonlinear dynamic system composed of product trigonometric functions and studies its chaotic characteristics. Through the mathematical derivation of the system’s period, the analysis of the necessary conditions at the fixed point, the experimental drawing of the Lyapunov exponential graph and the branch graph of the system, it is proved that the system has larger chaotic interval and stronger chaotic characteristics. The parameters of the proposed dynamic system are generated randomly, and then the chaotic sequence can be generated. The chaotic sequence is used to encrypt the digital image, a good encryption effect is obtained, and there is a large key space. At the same time, the motion of the particles in the space magnetic field is simulated, which further proves that the trigonometric system has strong chaotic characteristics.

Dynamic Response Analyses of Rabbit Knee Joint

1999 ◽  
Author(s):  
M. Kasra ◽  
M. D. Grynpas ◽  
A. Shirazi-Adl
Keyword(s):  
Knee Joint ◽  
Dynamic System ◽  
Experimental Studies ◽  
Knee Injuries ◽  
Nonlinear Dynamic System ◽  
Rabbit Knee ◽  
Prediction And Prevention ◽  
Joint Load ◽  
Dynamic Loading Conditions ◽  
Knee Disorders

Abstract The knee joint is a complex nonlinear dynamic system. It is generally known that mechanical factors play an important role in the etiology of knee injuries and diseases such as osteoarthritis. While performing daily activities such as walking, running, and climbing as well as during occupational operations, the joint is exposed to vibrations and multiple impacts. During these activities, according to an individual’s condition (e.g., age, fitness, weight), the joint load and stiffness may reach critical limits initiating or accelerating different knee disorders. This is the case in athletes or workers during occupational activities (1). Therefore, understanding the dynamic characteristics of the knee joint is essential in prediction and prevention of knee disorders as well as in subsequent joint replacement and rehabilitation procedures. There have been very few reported experimental studies investigating the dynamic behavior of the whole knee joint as a dynamic system (2). The objective of this study was to investigate the changes in mechanical properties of the rabbit knee joint under different compressive dynamic loading conditions. Rabbit has frequently been used as an osteoarthritic knee model (3). The data obtained in this study, hence, will also be beneficial in our future studies of osteoarthritic rabbit models.

Control of Spin-Stabilized Spacecraft With Sloshing Fluid Stores

1992 ◽  
Vol 114 (4) ◽  
pp. 728-731 ◽  
Author(s):  
D. E. Hill ◽  
J. R. Baumgarten
Keyword(s):  
Dynamic Instability ◽  
Fluid Motion ◽  
Nonlinear Dynamic System ◽  
Linear Feedback ◽  
Control Law ◽  
Main Body ◽  
Spherical Pendulum ◽  
Linear Feedback Control ◽  
Highly Nonlinear ◽  
Body Dynamics

Spin-stabilized spacecraft with sloshing fluid stores are known to be a source of dynamic instability for certain spacecraft configurations. A time varying linear feedback control law was developed, using an equivalent spherical pendulum mechanical model of the fluid motion coupled to the main body dynamics, which stabilizes the highly nonlinear dynamic system within a large region of operation. The control law was also demonstrated to perform a pointing maneuver. A control design for a specific spacecraft is outlined and implemented by sensing only the main body angular rates and attitude.

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