Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 78
... sketched only for de / dt > 0 and 0 < 0 < π . — For 2g > E > 0 , all values of do not occur . Only angles such that Eg ( 1 cos 0 ) or equivalently cos 01 - E / g are valid . From Fig . 22-2 , where as sketched 0 < E < 2g , it is ...
... sketched only for de / dt > 0 and 0 < 0 < π . — For 2g > E > 0 , all values of do not occur . Only angles such that Eg ( 1 cos 0 ) or equivalently cos 01 - E / g are valid . From Fig . 22-2 , where as sketched 0 < E < 2g , it is ...
Page 95
... sketched in Fig . 26-4 . To locate the = V = dx dt + X -x m X m Figure 26-4 Isoclines for md2 x / dt2 = -kx . most general isocline , we look for the curve along which the slope of the solution is the constant 2 , dv / dx = λ . From ...
... sketched in Fig . 26-4 . To locate the = V = dx dt + X -x m X m Figure 26-4 Isoclines for md2 x / dt2 = -kx . most general isocline , we look for the curve along which the slope of the solution is the constant 2 , dv / dx = λ . From ...
Page 370
... sketched in Fig . 80-1 ( with Po 15 and P1 = 45 ) , where the flow - density curve is given by Fig . 68-2 . [ Hint : Since the shock velocity is approximately the average of the two density wave velocities ( see exercise 77.3 ) , the ...
... sketched in Fig . 80-1 ( with Po 15 and P1 = 45 ) , where the flow - density curve is given by Fig . 68-2 . [ Hint : Since the shock velocity is approximately the average of the two density wave velocities ( see exercise 77.3 ) , 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