Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 336
... Umax - ( 73.7 ) ( 73.8 ) From equation 73.6 the car starts moving with zero initial velocity ; it slowly accelerates . Its velocity is always less than umax . For very large t , the car approaches maximum velocity ; dx / dt → Umax as ...
... Umax - ( 73.7 ) ( 73.8 ) From equation 73.6 the car starts moving with zero initial velocity ; it slowly accelerates . Its velocity is always less than umax . For very large t , the car approaches maximum velocity ; dx / dt → Umax as ...
Page 374
... Umax 2x ( 1 - 20 ) . Dmax ) Furthermore the general expression for the shock velocity may be simplified as follows : dxs dt = Umax P2 - [ q ] 92-91 == P2 P1 P2 Pmax P2P1 – P1 ( 1 - P1 Pmax / or equivalently P2 dx , = Umax dt - P1 + - P ...
... Umax 2x ( 1 - 20 ) . Dmax ) Furthermore the general expression for the shock velocity may be simplified as follows : dxs dt = Umax P2 - [ q ] 92-91 == P2 P1 P2 Pmax P2P1 – P1 ( 1 - P1 Pmax / or equivalently P2 dx , = Umax dt - P1 + - P ...
Page 375
... Umax ( tu — T ) T ) = u ( po ) tu ( following from Fig . 82-5 ) or thus when tu = - umaxt Umax u ( po ) Umaxt Pmaxt , Umax Umax ( 1 Po Po ( 82.5 ) Pmax a very long time for light traffic , a shorter time for heavier traffic . t , can ...
... Umax ( tu — T ) T ) = u ( po ) tu ( following from Fig . 82-5 ) or thus when tu = - umaxt Umax u ( po ) Umaxt Pmaxt , Umax Umax ( 1 Po Po ( 82.5 ) Pmax a very long time for light traffic , a shorter time for heavier traffic . t , can ...
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 |
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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