Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 56
... example , economics , chemistry , and widely diverse fields of engineering and physics . As illustrated by the two equilibrium positions for a nonlinear pendulum , the concept of stability is not a difficult one . Basically , an ...
... example , economics , chemistry , and widely diverse fields of engineering and physics . As illustrated by the two equilibrium positions for a nonlinear pendulum , the concept of stability is not a difficult one . Basically , an ...
Page 164
... example , suppose the growth rate is a constant R。, but occurs with a delay ta . Then dN ( t ) dt = = R。N ( t — ta ) , ( 40.3 ) a linear delay - differential equation . If we apply the ideas behind logistic growth to the delay ...
... example , suppose the growth rate is a constant R。, but occurs with a delay ta . Then dN ( t ) dt = = R。N ( t — ta ) , ( 40.3 ) a linear delay - differential equation . If we apply the ideas behind logistic growth to the delay ...
Page 196
... example . However , if a , b , c , and d are real , it follows from equation 45.9 that any complex eigenvalues at least must be complex conjugates of each other . In the example to follow , we will illustrate how to obtain real ...
... example . However , if a , b , c , and d are real , it follows from equation 45.9 that any complex eigenvalues at least must be complex conjugates of each other . In the example to follow , we will illustrate how to obtain real ...
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