Motion Equations for the Ball and Beam and the Ball and Arc Systems

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Constance Lare ◽  
Warren N. White ◽  
Sanzida Hossain
Keyword(s):  
Dynamic Models ◽  
Controller Design ◽  
Equations Of Motion ◽  
Dimensionless Form ◽  
Dimensionless Numbers ◽  
Motion Equations ◽  
Systems Model ◽  
Consistent Manner ◽  
Simplifying Assumptions ◽  
The Impact

Abstract Presently, most derivations of the equations of motion for the ball and beam and ball and arc systems model the ball as a point mass. Other derivations apply assumptions related to the ball that lack physical justification. To understand fully the impact the ball has on the equations of motion and controller design, equations of motion are needed that stem from a derivation invoking few assumptions. At that point, simplifying assumptions applied in a consistent manner are possible. This paper derives the equations of motion for each mechanical system using fewer assumptions than what appears in the literature. The development then applies the assumptions needed to convert the derived dynamics to the well-used equations of motion seen in the literature. The presentation shows that some ball and beam models appearing in the literature do not stem from consistent assumptions or correct kinematics. Incorrect kinematics are also present in some of the ball and arc dynamic models. This paper also introduces dimensionless quantities to the dynamic equations of both systems rendering them in dimensionless form. Such formulations allow for comparisons between different systems through the size of the dimensionless quantities. The dimensionless systems are the means used to demonstrate that the equations of motion of each system are the same as the radius of the arc grows without bound. Finally, the paper shows that comparisons between different ball and beam models using these dimensionless numbers are now possible.

scholarly journals Diagonally dominant backstepping autopilot for aircraft with unknown actuator failures and severe winds

2014 ◽  
Vol 118 (1207) ◽  
pp. 1009-1038 ◽  
Author(s):  
S. Ismail ◽  
A. A. Pashilkar ◽  
R. Ayyagari ◽  
N. Sundararajan
Keyword(s):  
Dynamic Models ◽  
Controller Design ◽  
Design Method ◽  
Equations Of Motion ◽  
Control Surface ◽  
Actuator Failures ◽  
Time Scale Separation ◽  
Diagonally Dominant ◽  
Trajectory Following ◽  
And Control

Abstract A novel formulation of the flight dynamic equations is presented that permits a rapid solution for the design of trajectory following autopilots for nonlinear aircraft dynamic models. A robust autopilot control structure is developed based on the combination of the good features of the nonlinear dynamic inversion (NDI) method, integrator backstepping method, time scale separation and control allocation methods. The aircraft equations of motion are formulated in suitable variables so that the matrices involved in the block backstepping control design method are diagonally dominant. This allows us to use a linear controller structure for a trajectory following autopilot for the nonlinear aircraft model using the well known loop by loop controller design approach. The resulting autopilot for the fixed-wing rigid-body aircraft with a cascaded structure is referred to as the diagonally dominant backstepping (DDBS) controller. The method is illustrated here for an aircraft auto-landing problem under unknown actuator failures and severe winds. The requirement of state and control surface limiting is also addressed in the context of the design of the DDBS controller.

Monetary policy and the effect of the transfer of oil prices to inflation

2020 ◽  
pp. 41-50
Author(s):  
Ph. S. Kartaev ◽  
I. D. Medvedev
Keyword(s):  
Monetary Policy ◽  
Inflation Targeting ◽  
Dynamic Models ◽  
Oil Prices ◽  
Oil Price ◽  
Oil Price Shocks ◽  
Negative Effects ◽  
Price Shocks ◽  
Policy Regime ◽  
The Impact

The paper examines the impact of oil price shocks on inflation, as well as the impact of the choice of the monetary policy regime on the strength of this influence. We used dynamic models on panel data for the countries of the world for the period from 2000 to 2017. It is shown that mainly the impact of changes in oil prices on inflation is carried out through the channel of exchange rate. The paper demonstrates the influence of the transition to inflation targeting on the nature of the relationship between oil price shocks and inflation. This effect is asymmetrical: during periods of rising oil prices, inflation targeting reduces the effect of the transfer of oil prices, limiting negative effects of shock. During periods of decline in oil prices, this monetary policy regime, in contrast, contributes to a stronger transfer, helping to reduce inflation.

scholarly journals Online Reviews and Product Sales: The Role of Review Visibility

2021 ◽  
Vol 16 (4) ◽  
pp. 638-669
Author(s):  
Miriam Alzate ◽  
Marta Arce-Urriza ◽  
Javier Cebollada
Keyword(s):  
Decision Making ◽  
Dynamic Models ◽  
Generalized Method Of Moments ◽  
Online Reviews ◽  
Consumer Decision Making ◽  
Product Sales ◽  
The Impact ◽  
The Relationship ◽  
The Empirical Analysis

When studying the impact of online reviews on product sales, previous scholars have usually assumed that every review for a product has the same probability of being viewed by consumers. However, decision-making and information processing theories underline that the accessibility of information plays a role in consumer decision-making. We incorporate the notion of review visibility to study the relationship between online reviews and product sales, which is proxied by sales rank information, studying three different cases: (1) when every online review is assumed to have the same probability of being viewed; (2) when we assume that consumers sort online reviews by the most helpful mechanism; and (3) when we assume that consumers sort online reviews by the most recent mechanism. Review non-textual and textual variables are analyzed. The empirical analysis is conducted using a panel of 119 cosmetic products over a period of nine weeks. Using the system generalized method of moments (system GMM) method for dynamic models of panel data, our findings reveal that review variables influence product sales, but the magnitude, and even the direction of the effect, vary amongst visibility cases. Overall, the characteristics of the most helpful reviews have a higher impact on sales.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

scholarly journals Interconnections Accelerate Collapse in a Socio-Ecological Metapopulation

2019 ◽  
Vol 11 (7) ◽  
pp. 1852 ◽  
Author(s):  
Zachary Dockstader ◽  
Chris Bauch ◽  
Madhur Anand
Keyword(s):  
Theoretical Models ◽  
Ecological Sustainability ◽  
Human Populations ◽  
Metapopulation Model ◽  
Single Population ◽  
Metapopulation Structure ◽  
Model Dynamics ◽  
Simplifying Assumptions ◽  
Over Exploitation ◽  
The Impact

Over-exploitation of natural resources can have profound effects on both ecosystems and their resident human populations. Simple theoretical models of the dynamics of a population of human harvesters and the abundance of a natural resource being harvested have been studied previously, but relatively few models consider the effect of metapopulation structure (i.e., a population distributed across discrete patches). Here we analyze a socio-ecological metapopulation model based on an existing single-population model used to study persistence and collapse in human populations. Resources grow logistically on each patch. Each population harvests resources on its own patch to support population growth, but can also harvest resources from other patches when their own patch resources become scarce. We show that when populations are allowed to harvest resources from other patches, the peak population size is higher, but subsequent population collapse is significantly accelerated and across a broader parameter regime. As the number of patches in the metapopulation increases, collapse is more sudden, more severe, and occurs sooner. These effects persist under scenarios of asymmetry and inequality between patches. Our model makes simplifying assumptions in order to facilitate insight and understanding of model dynamics. However, the robustness of the model prediction suggests that more sophisticated models should be developed to ascertain the impact of metapopulation structure on socio-ecological sustainability.

scholarly journals Assessing the impact of widespread respirator use in curtailing COVID-19 transmission in the USA

2021 ◽  
Vol 8 (9) ◽  
pp. 210699
Author(s):  
Calistus N. Ngonghala ◽  
James R. Knitter ◽  
Lucas Marinacci ◽  
Matthew H. Bonds ◽  
Abba B. Gumel
Keyword(s):  
Dynamic Models ◽  
Effective Control ◽  
Natural Immunity ◽  
Third Wave ◽  
Respiratory Protection ◽  
The Third ◽  
Surgical Masks ◽  
The Usa ◽  
Baseline Levels ◽  
The Impact

Dynamic models are used to assess the impact of three types of face masks (cloth masks, surgical/procedure masks and respirators) in controlling the COVID-19 pandemic in the USA. We showed that the pandemic would have failed to establish in the USA if a nationwide mask mandate, based on using respirators with moderately high compliance, had been implemented during the first two months of the pandemic. The other mask types would fail to prevent the pandemic from becoming established. When mask usage compliance is low to moderate, respirators are far more effective in reducing disease burden. Using data from the third wave, we showed that the epidemic could be eliminated in the USA if at least 40% of the population consistently wore respirators in public. Surgical masks can also lead to elimination, but requires compliance of at least 55%. Daily COVID-19 mortality could be eliminated in the USA by June or July 2021 if 95% of the population opted for either respirators or surgical masks from the beginning of the third wave. We showed that the prospect of effective control or elimination of the pandemic using mask-based strategy is greatly enhanced if combined with other non-pharmaceutical interventions (NPIs) that significantly reduce the baseline community transmission. By slightly modifying the model to include the effect of a vaccine against COVID-19 and waning vaccine-derived and natural immunity, this study shows that the waning of such immunity could trigger multiple new waves of the pandemic in the USA. The number, severity and duration of the projected waves depend on the quality of mask type used and the level of increase in the baseline levels of other NPIs used in the community during the onset of the third wave of the pandemic in the USA. Specifically, no severe fourth or subsequent wave of the pandemic will be recorded in the USA if surgical masks or respirators are used, particularly if the mask use strategy is combined with an increase in the baseline levels of other NPIs. This study further emphasizes the role of human behaviour towards masking on COVID-19 burden, and highlights the urgent need to maintain a healthy stockpile of highly effective respiratory protection, particularly respirators, to be made available to the general public in times of future outbreaks or pandemics of respiratory diseases that inflict severe public health and socio-economic burden on the population.

scholarly journals "It Isn't All about You": The Management of ICT and Non-ICT Information Resources via Human Information Behaviour

2021 ◽  
Author(s):  
◽  
Paul Daniel Atkinson
Keyword(s):  
Activity Theory ◽  
Information And Communication Technologies ◽  
Time Management ◽  
Information Seeking ◽  
Research Question ◽  
Information Use ◽  
Information Behaviour ◽  
Systems Model ◽  
Wide Range ◽  
The Impact

<p>"Applications that gather dust... Technologies no one understands... Information that's ignored... [thus, there is still very much a need to] pay attention to Information behaviour" (Davenport, 1997, p.2). Human Information Behaviour is as important a concept today as it has ever been, as there are still millions of dollars going into improving information technology. While information seeking behaviour has been rigorously studied over the years, information use has not received the same attention. Neither has the IT artefact or choice of such technologies at the hands of users of information. This research paper aims to produce a taxonomy of the information use behaviours and ICT and non-ICT resource use of IT academics through a qualitative study involving both observation (incorporating thinking aloud) and structured face-to-face interview techniques. The research question asks "How do IT Academics manage the integration between various Information and Communication Technologies (ICT) and non-ICT sources to support their information behaviours (IB) and, therefore, achieve their desired outcome? We observed and interviewed six IT academics carrying out their normal working activities, looking into actual information events as they occurred, information outcomes, information behaviours, and the technologies used by academics in their daily interactions with information. We developed a systems model, informed by activity theory, to frame the discussion. What was uncovered by the study was a tendency for academics to converge on a single technology - that of the laptop. This together with email was what academics tended to prefer to use, both at the office and in their homes; a surprising find as it was assumed that there would be a plethora of different ICTs in use. We found that technologies contributed to a blurring of the work/life equilibrium for many academics. Academics did exhibit a wide range of behaviours in their laptop and email use. Many of them were relatively unproductive, and involved moving information from one place, or one form to another, and finally ending in deletion rather than active use. Many of our interviewees reflected a need to use their time wisely through time management, and the impact of email on time management. These results also yielded the justification of Activity Theory which was used in the study, and of the systems framework which was constructed for the study. The study also confirmed the importance of environmental influences on academic's working lives, which tended to create a somewhat cyclic nature to their information events. Overall, it was not clear that patterns of use of ICTs contributed to effective information use behaviour by IT academics.</p>

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