Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 260
... car might refer , for example , to the center of the car . In a highway situation with many cars each is designated by an x¡ ( t ) , as shown in Fig . 57-1 . X4 X3 X2 X1 Figure 57-1 Highway ( position of cars denoted by x¿ ) . There are ...
... car might refer , for example , to the center of the car . In a highway situation with many cars each is designated by an x¡ ( t ) , as shown in Fig . 57-1 . X4 X3 X2 X1 Figure 57-1 Highway ( position of cars denoted by x¿ ) . There are ...
Page 267
... cars not completely in a given region at a fixed time . Perhaps estimates of fractional cars could be used or perhaps a car is counted only if its center is in the region . These measurements yield the number of cars in a given length ...
... cars not completely in a given region at a fixed time . Perhaps estimates of fractional cars could be used or perhaps a car is counted only if its center is in the region . These measurements yield the number of cars in a given length ...
Page 276
... cars between x = a and x b might still change in time . The number decreases due to cars leaving the region at x = b , and the number increases as a result of cars entering the region at x = a . Assuming that no cars are created or ...
... cars between x = a and x b might still change in time . The number decreases due to cars leaving the region at x = b , and the number increases as a result of cars entering the region at x = a . Assuming that no cars are created or ...
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