Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 331
... light changes from red to green , the maximum flow occurs at the light , x = stays there for all future time . This suggests a simple experiment to measure the maximum flow . Position an observer at a traffic light . Wait until the ...
... light changes from red to green , the maximum flow occurs at the light , x = stays there for all future time . This suggests a simple experiment to measure the maximum flow . Position an observer at a traffic light . Wait until the ...
Page 372
... light or an accident ) . We will determine the effect of traffic being momentarily stopped . * The initial density is a constant Po , p ( x , 0 ) = Po . After the light turns red , cars line up behind the light in a manner we have ...
... light or an accident ) . We will determine the effect of traffic being momentarily stopped . * The initial density is a constant Po , p ( x , 0 ) = Po . After the light turns red , cars line up behind the light in a manner we have ...
Page 381
... light passes the light . traffic started ) to the uniform density P .. An observer at the traffic light would mark this as the time when the traffic jam has finally cleared away . This time can be quite long . As Richards noted , if po ...
... light passes the light . traffic started ) to the uniform density P .. An observer at the traffic light would mark this as the time when the traffic jam has finally cleared away . This time can be quite long . As Richards noted , if po ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др