Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 308
... wave velocity can thus be positive or negative ! In the next section we will attempt to describe what a density wave is , in particular , what it means for the velocity of a density wave to be negative ! 67.1 . Suppose that q Road ...
... wave velocity can thus be positive or negative ! In the next section we will attempt to describe what a density wave is , in particular , what it means for the velocity of a density wave to be negative ! 67.1 . Suppose that q Road ...
Page 312
... wave velocity and the rope velocity , just as there are car velocity and density wave velocity for traffic flow problems . In traffic flow problems , there are two important velocities : one the velocity of individual cars and the other ...
... wave velocity and the rope velocity , just as there are car velocity and density wave velocity for traffic flow problems . In traffic flow problems , there are two important velocities : one the velocity of individual cars and the other ...
Page 332
... < 0 ) . The maximum flow occurs when the density wave is stationary ( density wave velocity equals zero ) . For this ρ max ρ Figure 73-2 Parabolic flow - density relationship . linear velocity - density curve , the density at which 332 ...
... < 0 ) . The maximum flow occurs when the density wave is stationary ( density wave velocity equals zero ) . For this ρ max ρ Figure 73-2 Parabolic flow - density relationship . linear velocity - density curve , the density at which 332 ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero