Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 171
... Constant Coefficient Difference Equations The stability of an equilibrium solution of a nonlinear autonomous second order difference equation is determined from its linearization , a constant coefficient difference equation . An ...
... Constant Coefficient Difference Equations The stability of an equilibrium solution of a nonlinear autonomous second order difference equation is determined from its linearization , a constant coefficient difference equation . An ...
Page 273
... constant velocity u 。 with a constant density p 。, as shown in Fig . 59-1 . Since each car Observer Figure 59-1 Constant flow of cars . moves at the same speed , the distance between cars remains constant . Hence the traffic density ...
... constant velocity u 。 with a constant density p 。, as shown in Fig . 59-1 . Since each car Observer Figure 59-1 Constant flow of cars . moves at the same speed , the distance between cars remains constant . Hence the traffic density ...
Page 387
... constant Bo , then the traffic density at all times must satisfy the following partial differential equation : + It ... Constantly Entering Cars CONSTANTLY ENTERING CARS 387*
... constant Bo , then the traffic density at all times must satisfy the following partial differential equation : + It ... Constantly Entering Cars CONSTANTLY ENTERING CARS 387*
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