Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 323
... moving observers ( possibly far apart ) , both moving at the same velocity V , such that the number of cars the first observer passes is the same as the number passed by the second observer . ( a ) Show that V = △ q | △ p . ( b ) Show ...
... moving observers ( possibly far apart ) , both moving at the same velocity V , such that the number of cars the first observer passes is the same as the number passed by the second observer . ( a ) Show that V = △ q | △ p . ( b ) Show ...
Page 349
... moving boundary ( the flow relative to a moving coordinate system ) is p ( x , t ) ( u ( x ,, t ) — dx , ) = q ( x ,, 1 ) — p ( x1 , 1 ) dx . — ( If the boundary moves with the car velocity , then no cars pass the moving boundary . ) A ...
... moving boundary ( the flow relative to a moving coordinate system ) is p ( x , t ) ( u ( x ,, t ) — dx , ) = q ( x ,, 1 ) — p ( x1 , 1 ) dx . — ( If the boundary moves with the car velocity , then no cars pass the moving boundary . ) A ...
Page 384
... ( moving at density po ) in the three - lane highway is less than the two - lane road's total capacity . ( b ) Assume that the initial density is such that the total flow ( moving at density po ) in the three - lane highway is more than ...
... ( moving at density po ) in the three - lane highway is less than the two - lane road's total capacity . ( b ) Assume that the initial density is such that the total flow ( moving at density po ) in the three - lane highway is more than ...
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