Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 95
... indicate in Fig . 26-5 some of these other isoclines . Any solution must be tangent to the slashes . In this manner a solution in the phase plane can be sketched ( as indicated by the darkened curve in Fig . 26-5 ) . In particular ...
... indicate in Fig . 26-5 some of these other isoclines . Any solution must be tangent to the slashes . In this manner a solution in the phase plane can be sketched ( as indicated by the darkened curve in Fig . 26-5 ) . In particular ...
Page 344
... indicate a sim- ple explanation for the fascinating wave phenomena of automobile brake lights . Have you ever been traveling in heavy traffic on a highway and observed that after someone applies their brake ( lighting the taillight ) a ...
... indicate a sim- ple explanation for the fascinating wave phenomena of automobile brake lights . Have you ever been traveling in heavy traffic on a highway and observed that after someone applies their brake ( lighting the taillight ) a ...
Page 355
... indicate that characteristics intersect each other whether the initial uniform traffic is light or heavy : t X x = 0 ... indicating that the method of characteristics yields a multivalued solution to the partial differential equa- tion ...
... indicate that characteristics intersect each other whether the initial uniform traffic is light or heavy : t X x = 0 ... indicating that the method of characteristics yields a multivalued solution to the partial differential equa- tion ...
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