Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 278
... limit as △ a → 0 : - [ **** p ( x , t ) dx = lim 9 ( a , t ) a Ca + 1 lim Aa - 0 Ət -Aa a Aa → 0 - q ( a + △ a , t ) -Δα . ( 60.4b ) The right - hand side of equation 60.4b is exactly the definition of the deriva- tive of q ( a , t ) ...
... limit as △ a → 0 : - [ **** p ( x , t ) dx = lim 9 ( a , t ) a Ca + 1 lim Aa - 0 Ət -Aa a Aa → 0 - q ( a + △ a , t ) -Δα . ( 60.4b ) The right - hand side of equation 60.4b is exactly the definition of the deriva- tive of q ( a , t ) ...
Page 289
... limit , and so on ) in order to maximize the flow on a given roadway . The largest flow q = pu would occur if cars were bumper to bumper ( p = Pmax ) moving at the speed limit ( u = Umax ) . Clearly this is not safe ( is that clear ...
... limit , and so on ) in order to maximize the flow on a given roadway . The largest flow q = pu would occur if cars were bumper to bumper ( p = Pmax ) moving at the speed limit ( u = Umax ) . Clearly this is not safe ( is that clear ...
Page 349
... limit from the left , f ( x , ̄ ) . However , both limits must exist . For example , see Fig . 77-2 . f ( x , - ) f ( x + ) Figure 77-2 Jump discontinuity . Xs † The terminology , shock wave , is introduced because of the analogous ...
... limit from the left , f ( x , ̄ ) . However , both limits must exist . For example , see Fig . 77-2 . f ( x , - ) f ( x + ) Figure 77-2 Jump discontinuity . Xs † The terminology , shock wave , is introduced because of the analogous ...
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