Instability and Chaos in Quadruped Gallop

1994 ◽  
Vol 116 (4) ◽  
pp. 1096-1101 ◽  
Author(s):  
P. Nanua ◽  
K. J. Waldron
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
The Body ◽  
Main Body ◽  
Viscous Damper ◽  
System Parameters ◽  
Constant Stiffness ◽  
Speed Controller ◽  
Symmetry Principles ◽  
The Stability

A dynamic model for the two-dimensional quadruped has been developed. The main body is modelled as a rigid bar and each leg consists of a constant stiffness spring, a viscous damper and a force actuator. Based on symmetry principles, a controller has been devised that will enable the quadruped to gallop at constant speed. The controller consists of two parts: an energy controller which will apply the required amount of force through the legs, and the speed controller that will control the forward speed by appropriately placing the legs. It will be shown that the body pitch need not be explicitly controlled. The stability of this controller will be examined using Poincare maps. Stable systems show either periodic or quasi-periodic response. This system also exhibits chaotic behavior and chaotic response results in instability. The stability of the system with changes in the initial conditions, as well as variations in the system parameters, will also be examined. It will be shown that the system is stable for a range of leg stiffnesses. Outside this range, the system shows chaotic behavior.

Instability and Chaos in Quadruped Gallop

1992 ◽  
Author(s):  
Prabjot Nanua ◽  
Kenneth J. Waldron
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
The Body ◽  
Main Body ◽  
Viscous Damper ◽  
System Parameters ◽  
Constant Stiffness ◽  
Speed Controller ◽  
Symmetry Principles ◽  
The Stability

Abstract A dynamic model for the two dimensional quadruped has been developed. The main body is modelled as a rigid bar and each leg consists of a constant stiffness spring, a viscous damper and a force actuator. Based on symmetry principles, a controller has been devised that will enable the quadruped to gallop at constant speed. The controller consists of two parts: an energy controller which will apply the required amount of force through the legs, and the speed controller that will control the forward speed by appropriately placing the legs. It will be shown that the body pitch need not be explicitly controlled. The stability of this controller will be examined using Poincare maps. Stable systems show either periodic or quasi-periodic response. This system also exhibits chaotic behavior and chaotic response leads to instability. The stability of the system with changes in the initial conditions, as well as variations in the system parameters, will also be examined. It will be shown that the system is stable for a range of leg stiffnesses. Outside this range, the system shows chaotic behavior.

scholarly journals Stability, Bifurcation, Chaos : Discrete Prey Predator Model with Step Size

2019 ◽  
Vol 9 (1) ◽  
pp. 3382-3387 ◽  
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Equilibrium States ◽  
Phase Portraits ◽  
Step Size ◽  
Dynamical Nature ◽  
Predator Model ◽  
The Stability ◽  
Parameter Values ◽  
Bifurcation Chaos

In this work titled Stability, Bifurcation, Chaos: Discrete prey predator model with step size, by Forward Euler Scheme method the discrete form is obtained. Equilibrium states are calculated and the stability of the equilibrium states and dynamical nature of the model are examined in the closed first quadrant 2 R with the help of variation matrix. It is observed that the system is sensitive to the initial conditions and also to parameter values. The dynamical nature of the model is investigated with the assistance of Lyapunov Exponent, bifurcation diagrams, phase portraits and chaotic behavior of the system is identified. Numerical simulations validate the theoretical observations.

scholarly journals ESTUDO DO COMPORTAMENTO DINÂMICO DO MODELO NEURONAL DE HINDMARSH-ROSE

2019 ◽  
Vol 11 (4) ◽  
pp. 122-130
Author(s):  
RaildoSantos de Lima ◽  
Fábio Roberto Chavarette ◽  
Luiz Gustavo Pereira Roéfero Roéfero
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Nerve Impulse ◽  
Neuronal Model ◽  
Random Behavior ◽  
Highly Sensitive ◽  
Real Neuron ◽  
Hr Model ◽  
Biological Neuron ◽  
The Stability

Based on the Hindmarsh-Rose (RH) neuronal model for nerve impulse transmission, this paper aims to study the properties and dynamic behavior of the non-linear chaotic system that describes neuronal bursting in a single neuron. On the part of bioengineering, there is great motivation in the study of the HR model because it is well representative of the biological neuron, being able to simulate several behaviors of a real neuron, among them periodic, aperiodic and chaotic behavior. The literature suggests that the chaotic behaviorrepresents in the human being the epileptic or convulsive state. Through computer simulations, considering the system parameters, it was analyzed that the stability is highly sensitive to the initial conditions and producing oscillations, more so, when the oscillation increases the random behavior tends to increase making the system unpredictable.

CHAOTIC ROTATIONS OF AN ASYMMETRIC BODY WITH TIME-DEPENDENT MOMENTS OF INERTIA AND VISCOUS DRAG

2003 ◽  
Vol 13 (02) ◽  
pp. 393-409 ◽  
Author(s):  
M. IÑARREA ◽  
V. LANCHARES ◽  
V. M. ROTHOS ◽  
J. P. SALAS
Keyword(s):  
Aerodynamic Drag ◽  
Chaotic Behavior ◽  
Center Of Mass ◽  
The Body ◽  
Time Dependent ◽  
Viscous Drag ◽  
Moments Of Inertia ◽  
System Parameters ◽  
Higher Dimensional ◽  
Analytical Criterion

We study the dynamics of a rotating asymmetric body under the influence of an aerodynamic drag. We assume that the drag torque is proportional to the angular velocity of the body. Also we suppose that one of the moments of inertia of the body is a periodic function of time and that the center of mass of the body is not modified. Under these assumptions, we show that the system exhibits a transient chaotic behavior by means of a higher dimensional generalization of the Melnikov's method. This method give us an analytical criterion for heteroclinic chaos in terms of the system parameters. These analytical results are confirmed by computer numerical simulations of the system rotations.

scholarly journals Kinematic and Aerodynamic Investigation of the Butterfly in Forward Free Flight for the Butterfly-Inspired Flapping Wing Air Vehicle

2021 ◽  
Vol 11 (6) ◽  
pp. 2620
Author(s):  
Yixin Zhang ◽  
Xingjian Wang ◽  
Shaoping Wang ◽  
Wenhao Huang ◽  
Qiwang Weng
Keyword(s):  
High Speed ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Flapping Wing ◽  
The Body ◽  
Main Body ◽  
Free Flight ◽  
Forward Flight ◽  
The Stability ◽  
Generation Mechanisms

To ensure the stability of flight, the butterfly needs to flap its wings and simultaneously move its main body to achieve all kinds of flying motion, such as taking off, hovering, or reverse flight. The high-speed camera is used to record the swing of the abdomen, the movement of the wings, and the pitch angle of the body for butterflies during their free flight; the comprehensive biokinetic observations show that the butterfly’s wings and body are coupled in various flight states. The swing of the abdomen and the flap of the fore wing affect the pitch motion significantly. For theoretical analysis of the butterfly flight, a three-dimensional multi-rigid butterfly model based on real butterfly dimension is established, and the aerodynamic of the butterfly flight is simulated and analyzed via computational fluid dynamics methods to obtain an optimal kinematic model of butterfly forward flight. Moreover, the formation and development of three-dimensional vortex structures in the forward flight are also presented. The detailed structures of vortices and their dynamic behavior show that the wing’s flap and the abdominal swing play a key role in reorienting and correcting the “clap and peel” mechanism, and the force generation mechanisms are evaluated. The research indicates that longitudinal flight performance is mainly related to the kinematic parameters of the wing and body, and it can lead to the development of butterfly-inspired flapping wing air vehicles.

scholarly journals Stability Analysis of the Chaotic Lorenz System with a State-Feedback Controller

2021 ◽  
Author(s):  
Dan Jones
Keyword(s):  
Strange Attractor ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Geometric Approach ◽  
Stable Equilibrium Point ◽  
The Lorenz System ◽  
The Stability ◽  
Parameter Values

The Lorenz model is considered a benchmark system in chaotic dynamics in that it displays extraordinary sensitivity to initial conditions and the strange attractor phenomenon. Even though the system tends to amplify perturbations, it is indeed possible to convert a strange attractor to a non-chaotic one using various control schemes. In this work it is shown that the chaotic behavior of the Lorenz system can be suppressed through the use of a feedback loop driven by a quotient controller. The stability of the controlled Lorenz system is evaluated near its equilibrium points using Routh-Hurwitz testing, and the global stability of the controlled system is established using a geometric approach. It is shown that the controlled Lorenz system has only one globally stable equilibrium point for the set of parameter values under consideration.

THE CHARACTERISTICS OF ARTIFICIAL RICE WITH SEAWEED Eucheuma cottonii ADDITION AS A DIETARY FIBER SOURCE

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
Natalia Prodiana Setiawati ◽  
Joko Santoso ◽  
Sri Purwaningsih
Keyword(s):  
Blood Glucose ◽  
Dietary Fiber ◽  
Dietary Fibre ◽  
Extrusion Process ◽  
The Body ◽  
Starch Digestibility ◽  
Food Commodities ◽  
The Stability ◽  
Extrusion Technology ◽  
Eucheuma Cottonii

The utilization of local food commodities such as corn and cassava with seaweed addition as a dietary fiber source for producing artificial rice through extrusion technology is an  alternative for food diversification. The research was carried out to find out the best composition (rice, corn, cassava, and seaweed) and temperature of extrusion process on making artificial rice and the influence of dietary fibre on sensory properties and physicochemical. The composition of rice, corn, and cassava in proportion  of 1:3:1 with 20% seaweed, Eucheuma cottonii, addition and temperature extruder of 90 °C were selected as the best product for artificial rice. The  sensory evaluation was 8.02±0.21 (people’s preference). In physicochemical properties, dietary fiber significantly affected on low bulk density and starch digestibility. This condition is very good for health especially in maintaining the stability of blood glucose in the body. Keywords: artificial rice, composition, extrusion, seaweed, dietary fibre, temperature

Substantiation the machine with a basket for the application of mineral fertilizers and other bulk materials with the upper arrangement of the feeding device

2019 ◽  
pp. 37-43
Author(s):  
Fesenko, H.
Keyword(s):  
Fat Body ◽  
Mineral Fertilizer ◽  
The Body ◽  
Mineral Fertilizers ◽  
Analytical Mechanics ◽  
Bulk Materials ◽  
The Stability ◽  
Working Bodies ◽  
The Relationship ◽  
Stable Flow

Purpose. Increasing the uniformity of distribution of mineral fertilizers and other bulk materials due to the stability of their feed from the body to the spreading working bodies using the top feeder. Methods. The following methods are used to achieve this aim: the method of comparing the differences between individual groups of fertilizers, the method of analyzing the properties of a new technical system, the method of functional inventiveness, and the methods of theoretical and analytical mechanics. Results. The traction body of the conveyor of the upper feed of the body fat body machine for mineral fertilizers and other bulk materials was substantiated and the relationship between the height of its scrapers and the distance between them was established, as well as the nature of the mineral fertilizer pressure on the curvilinear wall of the body. In addition, the design of the advanced body fertilizer spreader is justified, which ensures a stable flow of fertilizers from the body due to the improvement of the top feeder. Conclusions. Because of the conducted researches, the advantages of machines equipped with top feeder are found. They create the conditions for the forced feeding mineral fertilizers and other loose materials from the container to the distribution bodies, which is a prerequisite for their evenness on the surface. With this, the imperfection of known machines with the top feeder constrains their introduction into agricultural production. On this account, a more thoroughly constructed solution of the body feeder of the top feed is substantiated, in which the conveyor provides a stable supply of fertilizers from the body with reduced energy consumption during operation. Keywords: analysis, feed, upper device, conveyor, stability, fertilizers, flow ability, body.

Novel Nanolipoidal Systems for the Management of Skin Cancer

2020 ◽  
Vol 14 (2) ◽  
pp. 108-125
Author(s):  
Apoorva Singh ◽  
Nimisha
Keyword(s):  
Skin Cancer ◽  
Survival Rates ◽  
Cancer Therapeutics ◽  
The Body ◽  
Surgical Removal ◽  
The Novel ◽  
Skin Cancers ◽  
Recent Developments ◽  
Abnormal Cells ◽  
The Stability

: Skin cancer, among the various kinds of cancers, is a type that emerges from skin due to the growth of abnormal cells. These cells are capable of spreading and invading the other parts of the body. The occurrence of non-melanoma and melanoma, which are the major types of skin cancers, has increased over the past decades. Exposure to ultraviolet radiations (UV) is the main associative cause of skin cancer. UV exposure can inactivate tumor suppressor genes while activating various oncogenes. The conventional techniques like surgical removal, chemotherapy and radiation therapy lack the potential for targeting cancer cells and harm the normal cells. However, the novel therapeutics show promising improvements in the effectiveness of treatment, survival rates and better quality of life for patients. Different methodologies are involved in the skin cancer therapeutics for delivering the active ingredients to the target sites. Nano carriers are very efficient as they have the ability to improve the stability of drugs and further enhance their penetration into the tumor cells. The recent developments and research in nanotechnology have entitled several targeting and therapeutic agents to be incorporated into nanoparticles for an enhancive treatment of skin cancer. To protect the research works in the field of nanolipoidal systems various patents have been introduced. Some of the patents acknowledge responsive liposomes for specific targeting, nanocarriers for the delivery or co-delivery of chemotherapeutics, nucleic acids as well as photosensitizers. Further recent patents on the novel delivery systems have also been included here.

The Tangled Tale of Phase Space

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Three Body Problem ◽  
Henri Poincaré ◽  
History Of ◽  
The Stability ◽  
Three Body ◽  
Space Phase ◽  
Central Paradigm ◽  
System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

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