Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 45
... direction of Ô , dx dt = L αθ θ . dt ( 14.4b ) The magnitude of the velocity is L ( de / dt ) , if motion lies along the circum- ference of a circle . Why is it obvious that if L is constant , then the velocity is in the direction ...
... direction of Ô , dx dt = L αθ θ . dt ( 14.4b ) The magnitude of the velocity is L ( de / dt ) , if motion lies along the circum- ference of a circle . Why is it obvious that if L is constant , then the velocity is in the direction ...
Page 49
... direction is a . Is this reasonable ? ( d ) If is independent of t , sketch possible trajectories . From part ( b ) , show that the acceleration is in the correct direction . 14.3 . Consider a mass m located at x = xî + yj and only ...
... direction is a . Is this reasonable ? ( d ) If is independent of t , sketch possible trajectories . From part ( b ) , show that the acceleration is in the correct direction . 14.3 . Consider a mass m located at x = xî + yj and only ...
Page 386
... direction . Hence the charac- teristics themselves are no longer straight lines ! The density waves do not move at a constant velocity . The partial differential equation has been reduced to a system of two ordinary differential ...
... direction . Hence the charac- teristics themselves are no longer straight lines ! The density waves do not move at a constant velocity . The partial differential equation has been reduced to a system of two ordinary differential ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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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