Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 267
... 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 of roadway , which might ...
... 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 of roadway , which might ...
Page 330
... given position on the roadway in the region of fanlike characteristics . Given t and x , the slope of the straight line from the origin to the point ( t , x ) in Fig . 72-11 equals dq / dp . Thus this straight line must have the same ...
... given position on the roadway in the region of fanlike characteristics . Given t and x , the slope of the straight line from the origin to the point ( t , x ) in Fig . 72-11 equals dq / dp . Thus this straight line must have the same ...
Page 333
... given by dq dp = X t since they start from x = 0 at t = 0. For the linear velocity - density relation- ship , the density wave velocity is given by equation 73.3 and hence max ( 1 - 2P ) . X = Umax t Solving for p yields Pmax い Pmax ...
... given by dq dp = X t since they start from x = 0 at t = 0. For the linear velocity - density relation- ship , the density wave velocity is given by equation 73.3 and hence max ( 1 - 2P ) . X = Umax t Solving for p yields Pmax い Pmax ...
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