Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 144
... occurs in time interval △ t , or the population was N at time t and no births occur during At . We have ignored the possibility of two or more births from different individuals ( in exercise 36.2 , it is shown that this assumption is a ...
... occurs in time interval △ t , or the population was N at time t and no births occur during At . We have ignored the possibility of two or more births from different individuals ( in exercise 36.2 , it is shown that this assumption is a ...
Page 365
... occur immediately . Let us attempt to calculate when a shock first occurs . Suppose that the first shock occurs at t = T , due to the intersection of two characteristics initially a distance Ax ( not necessarily small ) apart , one ...
... occur immediately . Let us attempt to calculate when a shock first occurs . Suppose that the first shock occurs at t = T , due to the intersection of two characteristics initially a distance Ax ( not necessarily small ) apart , one ...
Page 369
... occur only if dp / dx , < 0 for the entire highway ; the initial traffic density must be steadily decreasing . No shocks occur only if the initial traffic density is of the general form shown in Fig . 80-8 , in which case traffic will ...
... occur only if dp / dx , < 0 for the entire highway ; the initial traffic density must be steadily decreasing . No shocks occur only if the initial traffic density is of the general form shown in Fig . 80-8 , in which case traffic will ...
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