Physics
Dynamic Systems
Dynamic systems in physics refer to systems that change over time due to the interaction of various components or forces. These systems are characterized by their ability to exhibit complex behaviors and patterns, often influenced by feedback loops and non-linear relationships. Understanding dynamic systems is crucial for analyzing and predicting the behavior of physical phenomena, such as oscillations, chaos, and emergent properties.
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6 Key excerpts on "Dynamic Systems"
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eBook - ePub- Marcio Eisencraft, Romis Attux, Ricardo Suyama(Authors)
- 2018(Publication Date)
- CRC Press(Publisher)
3 Overview of dynamical systems and chaos Luiz H. A. Monteiro Escola de Engenharia da Universidade Presbiteriana Mackenzie Escola Politécnica da Universidade de São Paulo CONTENTS 3.1 State-variable representation and some terminology 3.2 Steady state and Lyapunov stability 3.3 Periodic and quasiperiodic solutions 3.4 Chaotic behavior 3.5 Structural stability and bifurcation 3.6 Examples: dynamics of PLLs 3.7 Concluding remarks 3.8 Acknowledgments Bibliography Dynamical Systems Theory (DST) is the branch of applied mathematics dedicated to qualitatively characterizing the long-term behavior of systems evolving according to difference and differential equations. DST has its roots in classical mechanics, a major area in physics dealing with dynamics, kinematics, and statics of solids and fluids. Classical mechanics is based on the premise that the future can be predicted from an accurate knowledge of the present; effects can be determined from its causes. Thus, predictability would be a logical consequence of causal determinism
eBook - ePubSustainability
A Systems Approach
- Tony Clayton, Nicholas Radcliffe(Authors)
- 2018(Publication Date)
- Routledge(Publisher)
Application . The whole point of developing a model is that it should help to answer questions and thereby inform policy. A good model will therefore generate information that is in a useful form.Models of linear systems usually attempt to provide a relatively precise specification of the system in a set of equations and so capture its behaviour. If the equations accurately reflect the structure of the system, it should be possible to model its behaviour with some precision. Most conventional economic models, for example, are of this type, typically involving hundreds of equations.16One of the interesting features of models of non-linear systems, by contrast, is that the essential system dynamics can sometimes be captured in a relatively small number of equations sometimes as few as two or three.It is clearly important and useful to simplify and capture the essential behaviour of a system in this way. It allows us to develop our understanding, test our assumptions and estimate the effects of particular decisions and actions on the model before risking them in the real world.Dynamic system behaviour
Very complex dynamic or adaptive systems, such as the weather, evolutionary processes or market operations, pose new kinds of modelling problems. It is very difficult to model and predict the behaviour of such complex systems.17 We do not yet have all the necessary techniques and tools. In general terms, however, it is clear that the pattern of connectedness between the elements of a dynamic system is centrally involved in determining the behaviour of such systems.Dynamical system behaviour is generally grouped into four classes, as follows:❑ Class 1 . Fixed, where the system is ‘frozen’.❑ Class 2 . Periodic, where the system runs through a fixed cycle.❑ Class 3
eBook - ePubDevelopmental Psychology
How Nature and Nurture Interact
- Keith Richardson(Author)
- 2005(Publication Date)
- Psychology Press(Publisher)
In addition, organismic development is an open system: it exchanges energy and matter with its environment. This property is crucial for two reasons. First, if the organism were a closed system the second law of thermodynamics would hold, and the energy in the system, the organism, would dissipate, so there would be no differentiated structure, just as ice, a result of the ‘development’, the self-organization of water between 0 and -4 degrees, is the same all over. Organisms can confound this principle only by reorganizing internally to become more effectively coupled to the environment, more differentiated. And this is the second property. This process of internal reorganization is the means whereby the organism becomes more differentiated, as it develops structures which couple it adaptively to the ecology. Indeed, that is what development is. This coupling, like evolving a skeleton to cope with gravity, or means of navigation based upon complex invariances in the movement of stars, or the sun, or learning a language, both constrains the ways in which interactions between the organism and environment can take place and afford others (I can walk but cannot fly, for instance, I can speak English as a first language, but not Japanese).Thirdly, because dynamic models focus on change over time they are better equipped for the analysis of process, of how change occurs, a matter we will look into in more detail in a separate section (p. 77 below). So as all Dynamic Systems have these characteristic properties, we can apply what has already been found about the properties of such systems to the study of human development. We can thereby move away from the sterile focus on stages, to transitions, the dynamics of change.Another obvious feature of these views lies in the unit of analysis used. It is assumed that the behaviour and function of any object, organism or phenomenon can be understood only in relation to the system of which it is a part. Systems have multiple components, so it is never assumed that any single preformed cause will determine outcomes. Rather, outcomes depend upon the particular pattern of interactions between the components, the factors. This is exactly the position we have reached both from the arguments adduced in Chapter 2
eBook - ePub- Noah D. Manring, Roger C. Fales(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
This chapter serves as a reference throughout the remainder of the text as conventional response characteristics are defined and as basic tools of dynamical analysis are employed in subsequent chapters. 3.2 MODELING 3.2.1 General To discuss the subject of control there is the presupposed existence of something that needs to be controlled. That something is generally referred to as the “plant” or the dynamic system through which the control objective is achieved. Without a rudimentary understanding of the nature and expected behavior of this dynamic system the subject of control becomes haphazard to say the least. As engineers we gain the understanding of Dynamic Systems through either experimental or analytical techniques of modeling. In this section we discuss the basics of modeling as it pertains to some relatively simple systems. These modeling examples are presented to illustrate analytical techniques and the basic structures of time varying systems that may be encountered within hydraulic control systems. 3.2.2 Mechanical Systems One of the most classical systems to be discussed in a dynamics textbook is the swinging pendulum shown in Figure 3-1. Using the basic principles of rigid body mechanics the equation of motion for this pendulum may be determined by summing moments about the pivot point and setting them equal to the time-rate-of-change of angular momentum for the moving body about this point. This result is written as Figure 3-1. The swinging pendulum. (3.1) where is the mass moment of inertia of the pendulum about point, is an external couple that is applied to the pendulum perhaps for the purposes of controlling its angular position, is a viscous drag coefficient, is the mass of the pendulum, is the gravitational constant, and the dimensions and are shown in Figure 3-1. This equation describes the physical behavior of the pendulum as it responds to the input effort. This equation is also called the model of the system or plant as shown in Figure 3-1
eBook - ePubMind, Brain and the Elusive Soul
Human Systems of Cognitive Science and Religion
- Mark Graves(Author)
- 2016(Publication Date)
- Routledge(Publisher)
7More recently, Len Troncale’s SSP model (Systems of Systems Processing) enables comparison of systems-linking propositions of over 80 systems processes observed in many complex systems.8 Processes used in this book (and explained later in context) include: attractors, boundary conditions, emergence, equilibrium, evolutionary processes, feedback, hierarchical structure, information flow, morphodynamics, network dynamics, phases, potential spaces or fields, restructuring rules, self-organizing processes, and stability processes.Computer scientists and biologists have explored systems within those disciplines that emphasize the significance of modularity and emergence in dynamic processing, which will prove relevant to modeling human systems. Herbert Simon showed that a modular architecture of complexity resulted in increased survivability when each module had at least a limited stability.9 Ilya Prigogine and his colleagues demonstrate the emergence of order through amplified, bifurcating fluctuations in non-linear thermoDynamic Systems.10 Stuart Kauffman argues that networks near the edge of chaos appear best able to coordinate complex activities.11 He also argues that an autonomous agent requires the ability to perform at least one thermodynamic work cycle.12 Current work in the field also includes systems analysis13 and object-oriented analysis and design.14Cybernetics
Norbert Wiener coined the term cybernetics to refer to “the science of control and communication in the animal and machine” from the Greek kybernetes (helmsman, governor, navigator, pilot, or rudder). Wiener examined teleological mechanisms (from Greek telos
eBook - ePub- Kamran Iqbal(Author)
- 2017(Publication Date)
- River Publishers(Publisher)
1 Physical System Models Learning Objectives- Obtain a physical system model from the component descriptions.
- Obtain the system transfer function from its differential equation model.
- Obtain a physical system model in state variable form.
- Linearize a nonlinear system model.
Physical systems of interest to engineers include electrical, mechanical, electromechanical, thermal, and fluid systems, among others. The behavior of these systems is mathematically described by the dynamic equations, i.e., ordinary linear differential equations (ODEs), if lumped parameter assumption is made.To model a system with interconnected components, individual component models can be assembled to formulate the system model. For electrical systems, these elements include resistors, capacitors, and inductors. For mechanical systems, these include inertias (masses), springs, and dampers (or friction elements). For thermal systems, these include thermal capacitance and thermal resistance. For fluid systems, these include the reservoir capacity and the flow resistance. All of these elements either store or dissipate energy, which gives rise to the time-varying or dynamic behavior of the systems.Modeling of the physical system behavior involves two kinds of variables: flow variables that ‘flow’ through the components, and across variables that are measured across the components. For the electrical circuits, voltage or potential is measured across the circuit nodes, whereas current or electrical charge flows through the circuit branches. In mechanical linkage systems, displacement and velocity are measured across the connecting nodes, whereas force or effort ‘flows’ through the linkages. For thermal and fluid systems, heat and mass serve as the flow variables, and temperature and pressure constitute the across variables.The relationship between flow and across variables defines the type of physical component being modeled. The elementary types are the resistive, the inductive, and the capacitive components. This terminology, taken from electrical circuits, also extends to other types of physical systems.
