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 |
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