Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 110
... illustrated by curve a . Others , more to the right , must turn towards the right as illustrated by curve b . Thus there must be a trajectory ( in between ) which " enters " the unstable equilibrium position . In a similar manner we can ...
... illustrated by curve a . Others , more to the right , must turn towards the right as illustrated by curve b . Thus there must be a trajectory ( in between ) which " enters " the unstable equilibrium position . In a similar manner we can ...
Page 269
... illustrated in Fig . 58-8 as a ' • ' 10 20 · • · · · 30 40 50 ......... · • · · • · 60 70 80 90 100 Figure 58-8 The traffic density " appears " as the density of ink dots . From the data ( or diagram ) we see that near the 20 mark cars ...
... illustrated in Fig . 58-8 as a ' • ' 10 20 · • · · · 30 40 50 ......... · • · · • · 60 70 80 90 100 Figure 58-8 The traffic density " appears " as the density of ink dots . From the data ( or diagram ) we see that near the 20 mark cars ...
Page 346
... illustrated in the figure . The sketched characteristics are moving forward ; the velocities of both density waves were assumed positive . This does not have to be so in general . However , in any situation in which the traffic becomes ...
... illustrated in the figure . The sketched characteristics are moving forward ; the velocities of both density waves were assumed positive . This does not have to be so in general . However , in any situation in which the traffic becomes ...
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