Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 85
... behavior of the nonlinear pendulum has been determined using the energy curves in the phase plane . Note that the curve in the phase plane for which E = 2g separates the phase plane into two distinct regions of entirely different ...
... behavior of the nonlinear pendulum has been determined using the energy curves in the phase plane . Note that the curve in the phase plane for which E = 2g separates the phase plane into two distinct regions of entirely different ...
Page 107
... behavior of the trajectories , we may further use the method of isoclines . Before doing so , however , we note that often the qualitative behavior can be more easily obtained by first analyzing the phase plane in the neighborhood of ...
... behavior of the trajectories , we may further use the method of isoclines . Before doing so , however , we note that often the qualitative behavior can be more easily obtained by first analyzing the phase plane in the neighborhood of ...
Page 227
... behavior of solutions of this nonlinear system of differential equations seem consistent with the observed oscillatory behavior ? EXERCISES 49.1 . Consider the following three - species ecosystem : dF dt ds - F ( a - cS ) -- dt S ( −k ...
... behavior of solutions of this nonlinear system of differential equations seem consistent with the observed oscillatory behavior ? EXERCISES 49.1 . Consider the following three - species ecosystem : dF dt ds - F ( a - cS ) -- dt S ( −k ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero