Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 85
... behavior of the nonlinear pendulum has been determined using the energy curves in the phase plane . Note that the curve in the phase plane for which E = 2g separates the phase plane into two distinct regions of entirely different ...
... behavior of the nonlinear pendulum has been determined using the energy curves in the phase plane . Note that the curve in the phase plane for which E = 2g separates the phase plane into two distinct regions of entirely different ...
Page 107
... behavior of the trajectories , we may further use the method of isoclines . Before doing so , however , we note that often the qualitative behavior can be more easily obtained by first analyzing the phase plane in the neighborhood of ...
... behavior of the trajectories , we may further use the method of isoclines . Before doing so , however , we note that often the qualitative behavior can be more easily obtained by first analyzing the phase plane in the neighborhood of ...
Page 227
... behavior of solutions of this nonlinear system of differential equations seem consistent with the observed oscillatory behavior ? EXERCISES 49.1 . Consider the following three - species ecosystem : dF dt ds - F ( a - cS ) -- dt S ( −k ...
... behavior of solutions of this nonlinear system of differential equations seem consistent with the observed oscillatory behavior ? EXERCISES 49.1 . Consider the following three - species ecosystem : dF dt ds - F ( a - cS ) -- dt S ( −k ...
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