Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 94
... slope . To indicate this small dashes are drawn with infinite slope on Fig . 26-3 . O is an isocline . Solution curves which cross the x - axis must be parallel to these dashes . v = V = dx dt X Figure 26-3 . Let us consider a specific ...
... slope . To indicate this small dashes are drawn with infinite slope on Fig . 26-3 . O is an isocline . Solution curves which cross the x - axis must be parallel to these dashes . v = V = dx dt X Figure 26-3 . Let us consider a specific ...
Page 98
... slope of the solution and the slope of an isocline . ) ( c ) Is it possible for the slope of an isocline to be the same as the slope of the solution ? In this case show that the isocline itself is a solution curve . 26.2 . Consider a ...
... slope of the solution and the slope of an isocline . ) ( c ) Is it possible for the slope of an isocline to be the same as the slope of the solution ? In this case show that the isocline itself is a solution curve . 26.2 . Consider a ...
Page 312
... slopes have the units of velocity , then the slope of the straight line characteristics are the same as the slope of the appropriate tangent to the Fundamental Diagram of Road Traffic . Thus if the traffic density is nearly Po , all the ...
... slopes have the units of velocity , then the slope of the straight line characteristics are the same as the slope of the appropriate tangent to the Fundamental Diagram of Road Traffic . Thus if the traffic density is nearly Po , all the ...
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 |
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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