Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 272
... assume that the distance between cars stays approximately the same over a distance that includes many cars . From this example , we see this is not always entirely the case ( in particular , this situation gets worse for less dense ...
... assume that the distance between cars stays approximately the same over a distance that includes many cars . From this example , we see this is not always entirely the case ( in particular , this situation gets worse for less dense ...
Page 360
... Assume that p1 is lighter traffic than po and both are light traffic ( i.e. , assume that u ( p ) Umax ( 1 - P / Pmax ) and thus p1 < Po < Pmax / 2 ) . Sketch = the density at various values of time . 78.9 . Do exercise 78.8 if po < P1 ...
... Assume that p1 is lighter traffic than po and both are light traffic ( i.e. , assume that u ( p ) Umax ( 1 - P / Pmax ) and thus p1 < Po < Pmax / 2 ) . Sketch = the density at various values of time . 78.9 . Do exercise 78.8 if po < P1 ...
Page 383
... Assume that u = - Umax ( 1 — P / Pmax ) and that the initial traffic density is p ( x , 0 ) = { P1 | x | > a Po x < a , where P1 > Po . Determine the density at later times . 82.3 . Assume u = Umax ( 1P / Pmax ) and the initial traffic ...
... Assume that u = - Umax ( 1 — P / Pmax ) and that the initial traffic density is p ( x , 0 ) = { P1 | x | > a Po x < a , where P1 > Po . Determine the density at later times . 82.3 . Assume u = Umax ( 1P / Pmax ) and the initial traffic ...
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