Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
From inside the book
Results 1-3 of 18
Page 314
... observer ( not necessarily in a car moving in traffic ) . Let the position of the observer be prescribed by x = x ( t ) . The traffic density measured by the observer depends on time , p , ( x ( t ) , t ) . The rate of change of this ...
... observer ( not necessarily in a car moving in traffic ) . Let the position of the observer be prescribed by x = x ( t ) . The traffic density measured by the observer depends on time , p , ( x ( t ) , t ) . The rate of change of this ...
Page 319
... observer moving in some prescribed fashion x ( t ) . The density of traffic at the observer changes in time as the observer moves about , dt df = of + dx of dp op . dt dx ( 71.2 ) By comparing equation 71.1 to equation 71.2 , it is seen ...
... observer moving in some prescribed fashion x ( t ) . The density of traffic at the observer changes in time as the observer moves about , dt df = of + dx of dp op . dt dx ( 71.2 ) By comparing equation 71.1 to equation 71.2 , it is seen ...
Page 323
... observer x2 minus the flow relative to the observer at x1 . ( Hint : See exercise 60.2 ) . 71.7 . Consider two moving observers ( possibly far apart ) , both moving at the same velocity V , such that the number of cars the first ...
... observer x2 minus the flow relative to the observer at x1 . ( Hint : See exercise 60.2 ) . 71.7 . Consider two moving observers ( possibly far apart ) , both moving at the same velocity V , such that the number of cars the first ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
80 other sections not shown
Other editions - View all
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