Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 210
... straight line trajectory is also of impor- tance . An easy method to determine all straight line trajectories ( assuming a book with the answer is not readily available ) is to substitute the assumed form of a straight line trajectory ...
... straight line trajectory is also of impor- tance . An easy method to determine all straight line trajectories ( assuming a book with the answer is not readily available ) is to substitute the assumed form of a straight line trajectory ...
Page 312
... straight lines with velocity c . If these characteristics are sketched in a space - time diagram such that slopes have the units of velocity , then the slope of the straight line characteristics are the same as the slope of the ...
... straight lines with velocity c . If these characteristics are sketched in a space - time diagram such that slopes have the units of velocity , then the slope of the straight line characteristics are the same as the slope of the ...
Page 321
... straight line , x = q ' ( pa ) t + k , where k , the x - intercept of this characteristic , equals & since at t = 0 , x = α . Thus the equation for this one characteristic is x = q ' ( pa ) t + α . Along this straight line , the traffic ...
... straight line , x = q ' ( pa ) t + k , where k , the x - intercept of this characteristic , equals & since at t = 0 , x = α . Thus the equation for this one characteristic is x = q ' ( pa ) t + α . Along this straight line , the traffic ...
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