Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 168
... decreases to either less than or greater than the carry- ing capacity , as shown in Fig . 40-4 . In a similar manner one can try to under- stand how the population may decrease even when it is less than the carrying capacity . It is the ...
... decreases to either less than or greater than the carry- ing capacity , as shown in Fig . 40-4 . In a similar manner one can try to under- stand how the population may decrease even when it is less than the carrying capacity . It is the ...
Page 271
... decreases ( as m increases ) again until the next car is located . The amplitude of the fluctuation decreases as the measuring interval gets longer . For extremely large measuring distances the 500 450 400 350 300 Traffic density 250 ...
... decreases ( as m increases ) again until the next car is located . The amplitude of the fluctuation decreases as the measuring interval gets longer . For extremely large measuring distances the 500 450 400 350 300 Traffic density 250 ...
Page 332
... decreases as p increases ( since d2q / dp2 < 0 , as will be shown ) . u max u = Umax ( 1 - p / Pmax ) u ( p ) velocity p density Pmax Figure 73-1 Linear velocity - density curve . In this case the traffic flow can be easily computed , q ...
... decreases as p increases ( since d2q / dp2 < 0 , as will be shown ) . u max u = Umax ( 1 - p / Pmax ) u ( p ) velocity p density Pmax Figure 73-1 Linear velocity - density curve . In this case the traffic flow can be easily computed , q ...
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