Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 55
... nonlinear pendulum also satisfies a differential equation of that form , since d20 L dt2 = g sin 0 . ( 17.2 ) Before solving these nonlinear ordinary differential equations , what properties do we expect the solution to have ? For small ...
... nonlinear pendulum also satisfies a differential equation of that form , since d20 L dt2 = g sin 0 . ( 17.2 ) Before solving these nonlinear ordinary differential equations , what properties do we expect the solution to have ? For small ...
Page 91
... Nonlinear Oscillations with Damping In the last few sections , we have analyzed the behavior of nonlinear oscillators neglecting frictional forces . We have found that the properties of nonlinear oscillators are quite similar to those ...
... Nonlinear Oscillations with Damping In the last few sections , we have analyzed the behavior of nonlinear oscillators neglecting frictional forces . We have found that the properties of nonlinear oscillators are quite similar to those ...
Page 114
... nonlinear ones with frictional forces . The behavior of the nonlinear systems we have analyzed seem qualitatively similar to linear ones . However , we have not made a complete mathematical analysis of all possible problems . By ...
... nonlinear ones with frictional forces . The behavior of the nonlinear systems we have analyzed seem qualitatively similar to linear ones . However , we have not made a complete mathematical analysis of all possible problems . By ...
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