Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 267
... measured over of a mile ( .4 kilometers ) of roadway at a fixed time , then a typical measurement might be : Distance along road ( in miles ) Number of cars 1-11 23 11-11 11-12 13-2 2420 16 8 Traffic density , number of cars per mile 92 ...
... measured over of a mile ( .4 kilometers ) of roadway at a fixed time , then a typical measurement might be : Distance along road ( in miles ) Number of cars 1-11 23 11-11 11-12 13-2 2420 16 8 Traffic density , number of cars per mile 92 ...
Page 268
... measured density is an extremely discontinuous function . On the other hand , if measurements of density are taken ... measured over intervals of distance that are not too small nor too large . If the measuring distance is too 1 0 1 2 2 ...
... measured density is an extremely discontinuous function . On the other hand , if measurements of density are taken ... measured over intervals of distance that are not too small nor too large . If the measuring distance is too 1 0 1 2 2 ...
Page 269
... measuring distance must be large enough so that many cars are contained therein , but small enough so that variations in densities can be measured . Let us illustrate by an example the significance of the measuring interval . Consider a ...
... measuring distance must be large enough so that many cars are contained therein , but small enough so that variations in densities can be measured . Let us illustrate by an example the significance of the measuring interval . Consider a ...
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