Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 321
... characteristics . V βγ α ' ( x . , t . ) Figure 71-4 Using characteristics to deter- mine the future traffic density . X The density wave velocity , dq / dp , is extremely important . At this velocity the traffic density stays the same ...
... characteristics . V βγ α ' ( x . , t . ) Figure 71-4 Using characteristics to deter- mine the future traffic density . X The density wave velocity , dq / dp , is extremely important . At this velocity the traffic density stays the same ...
Page 325
... characteristics are straight lines . In the x - t plane X dq ( p ) t + k , ( 72.3 ) where each characteristic may have a different integration constant k . Let us analyze all characteristics that intersect the initial data at x > 0 ...
... characteristics are straight lines . In the x - t plane X dq ( p ) t + k , ( 72.3 ) where each characteristic may have a different integration constant k . Let us analyze all characteristics that intersect the initial data at x > 0 ...
Page 365
... characteristics initially a distance Ax ( not necessarily small ) apart , one emanating from x1 , the other from x1 + Ax ; see Fig . 80-3 . If this is the first intersection , then no characteristics could have crossed at an earlier ...
... characteristics initially a distance Ax ( not necessarily small ) apart , one emanating from x1 , the other from x1 + Ax ; see Fig . 80-3 . If this is the first intersection , then no characteristics could have crossed at an earlier ...
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