DYNAMICS - 5 reference results
nonlinear dynamics, study of systems governed by equations in which a small change in one variable can induce a large systematic change; the discipline is more popularly known as chaos (see chaos theory). Unlike a linear system, in which a small change in one variable produces a small and easily quantifiable systematic change, a nonlinear system exhibits a sensitive dependence on initial conditions: small or virtually unmeasurable differences in initial conditions can lead to wildly differing outcomes. This sensitive dependence is sometimes referred to as the butterfly effect, the assertion that the beating of a butterfly's wings in Tokyo can eventually change the weather in New York City. Historically, in fact, one of the first nonlinear systems to be studied was the weather, which in the 1960s Edward Lorenz sought to model by a relatively simple set of equations. He discovered that the outcome of his model showed an acute dependence on initial conditions. Later work revealed that underlying such chaotic behavior are complex but often aesthetically pleasing geometric forms called strange attractors. Strange attractors exist in an imaginary space called phase space, in which the ordinary dimensions of real space are supplemented by additional dimensions for the momentum of the system under investigation. A strange attractor is a fractal, an object that exhibits self-similarity on all scales. A coastline, for instance, looks much the same up close or far away. Nonlinear dynamics has shown that even systems governed by simple equations can exhibit complex behavior. The evolution of nonlinear dynamics was made possible by the application of high-speed computers, particularly in the area of computer graphics, to innovative mathematical theories developed during the first half of the 20th cent. Three branches of study are recognized: classical systems in which friction and other dissipative forces are paramount, such as turbulent flow in a liquid or gas; classical systems in which dissipative forces can be neglected, such as charged particles in a particle accelerator; and quantum systems, such as molecules in a strong electromagnetic field. The tools of nonlinear dynamics have been used in attempts to better understand irregularity in such diverse areas as dripping faucets, population growth, the beating heart, and the economy.
See S. N. Rasband, Chaotic Dynamics of Nonlinear Systems (1990); A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (1992); S. J. Guastello, Chaos, Catastrophe, and Human Affairs: Applications of Nonlinear Dynamics to Work Organizations and Social Evolution (1995); A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (1995).
The Columbia Electronic Encyclopedia Copyright © 2004.
Licensed from Columbia University Press
Licensed from Columbia University Press
group dynamics: see group psychotherapy.
The Columbia Electronic Encyclopedia Copyright © 2004.
Licensed from Columbia University Press
Licensed from Columbia University Press
dynamics, branch of mechanics that deals with the motion of objects; it may be further divided into kinematics, the study of motion without regard to the forces producing it, and kinetics, the study of the forces that produce or change motion. Motion is caused by an unbalanced force acting on a body. Such a force will produce either a change in the body's speed or a change in the direction of its motion (see acceleration). The motion may be either translational (straight-line) or rotational. With the principles of dynamics one can solve problems involving work and energy and explain the pressure and expansion of gases, the motion of planets, and the behavior of flowing liquids and gases. Solids are rigid, having a definite shape, but fluids (liquids and gases) are not, and special branches of dynamics have been developed that treat the particular effects of forces and motions in fluids. These include fluid mechanics, the study of liquids in motion, and aerodynamics, the study of gases in motion. The applications of liquids both at rest and in motion are studied under hydraulics, a branch of engineering closely related to dynamics. The principles of dynamics may also be combined with the study of other phenomena, as in electrodynamics, the study of charges in motion.
The Columbia Electronic Encyclopedia Copyright © 2004.
Licensed from Columbia University Press
Licensed from Columbia University Press
Branch of mechanics that deals with the motion of objects in relation to force, mass, momentum, and energy. Dynamics can be divided into two branches, kinematics and kinetics. The foundations of dynamics were laid by Galileo, who derived the law of motion for falling bodies and was the first to recognize that all changes of velocity of a body are the result of forces. Isaac Newton formulated this observation in his second law of motion (see Newton's laws of motion).
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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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