Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 337
... Road Traffic shown in Fig . 73-10 . To determine car paths , small horizontal lines ( indicating no motion ) are sketched wherever p = Pmax . In addition , for example , we note that at x = 0 , the density is that corresponding to the ...
... Road Traffic shown in Fig . 73-10 . To determine car paths , small horizontal lines ( indicating no motion ) are sketched wherever p = Pmax . In addition , for example , we note that at x = 0 , the density is that corresponding to the ...
Page 384
... road's total capacity . ( b ) Assume that the initial density is such that the total flow ( moving at density po ) in the three - lane highway is more than the two - lane road's total capacity . ( Hints : A shock must occur , starting ...
... road's total capacity . ( b ) Assume that the initial density is such that the total flow ( moving at density po ) in the three - lane highway is more than the two - lane road's total capacity . ( Hints : A shock must occur , starting ...
Page 389
... road p ( x , 0 ) = 0 . ( 85.1 ) However , suppose cars are entering the road ( in some finite region 0 < x < x ) at a constant rate ẞ . per mile for all time , B ( x , t ) = ( 0 x < 0 = Bo 0 < x < XE 0 X > XE • What is the resulting ...
... road p ( x , 0 ) = 0 . ( 85.1 ) However , suppose cars are entering the road ( in some finite region 0 < x < x ) at a constant rate ẞ . per mile for all time , B ( x , t ) = ( 0 x < 0 = Bo 0 < x < XE 0 X > XE • What is the resulting ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др