Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 352
... shock condition as previously derived , equation 77.3 . Exercise 77.8 derives equation 77.3 from equation 77.5 differently . This shock velocity can also be graphically represented on the flow- density curve . Suppose that a shock ...
... shock condition as previously derived , equation 77.3 . Exercise 77.8 derives equation 77.3 from equation 77.5 differently . This shock velocity can also be graphically represented on the flow- density curve . Suppose that a shock ...
Page 353
... shock , Ax , / At , is again the same as derived before . In the next section we will consider traffic problems in which the partial differential equation predicts multivalued solutions , and hence shocks must be introduced to give ...
... shock , Ax , / At , is again the same as derived before . In the next section we will consider traffic problems in which the partial differential equation predicts multivalued solutions , and hence shocks must be introduced to give ...
Page 379
... shock strength ( of either shock ) tends to zero as t T- → ∞ . Further- more we have determined the rate at which the shock strengths tend to zero . More general discussions , beyond the scope of this text , show that in other ...
... shock strength ( of either shock ) tends to zero as t T- → ∞ . Further- more we have determined the rate at which the shock strengths tend to zero . More general discussions , beyond the scope of this text , show that in other ...
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