Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 171
... Constant Coefficient Difference Equations The stability of an equilibrium solution of a nonlinear autonomous second order difference equation is ... Constant Coefficient Difference Equations LINEAR CONSTANT COEFFICIENT DIFFERENCE EQUATIONS.
... Constant Coefficient Difference Equations The stability of an equilibrium solution of a nonlinear autonomous second order difference equation is ... Constant Coefficient Difference Equations LINEAR CONSTANT COEFFICIENT DIFFERENCE EQUATIONS.
Page 273
... constant velocity u 。 with a constant density p 。, as shown in Fig . 59-1 . Since each car Observer Figure 59-1 Constant flow of cars . moves at the same speed , the distance between cars remains constant . Hence the traffic density ...
... constant velocity u 。 with a constant density p 。, as shown in Fig . 59-1 . Since each car Observer Figure 59-1 Constant flow of cars . moves at the same speed , the distance between cars remains constant . Hence the traffic density ...
Page 387
... constant Bo , then the traffic density at all times must satisfy the following partial differential equation : + It ... Constantly Entering Cars CONSTANTLY ENTERING CARS 387*
... constant Bo , then the traffic density at all times must satisfy the following partial differential equation : + It ... Constantly Entering Cars CONSTANTLY ENTERING CARS 387*
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