Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
From inside the book
Results 1-3 of 81
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 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
80 other sections not shown
Other editions - View all
Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
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