Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 57
... analysis of equation 18.3 , known as a linearized stability analysis , shows that : 57 Sec . 18 Linearized Stability Analysis of an Equilibrium Solution.
... analysis of equation 18.3 , known as a linearized stability analysis , shows that : 57 Sec . 18 Linearized Stability Analysis of an Equilibrium Solution.
Page 75
... analysis , show that the position x oscillates around its equilibrium position . ( e ) If at t = to , x = xo and dx / dt = vo , then what is the maximum dis- placement from equilibrium ? Also , what velocity is the mass moving at when ...
... analysis , show that the position x oscillates around its equilibrium position . ( e ) If at t = to , x = xo and dx / dt = vo , then what is the maximum dis- placement from equilibrium ? Also , what velocity is the mass moving at when ...
Page 103
... analysis explains the behavior of the solution in the immediate vicinity of the equilibrium position . In the case in which the linearized stability analysis predicts the equilib- rium solution is unstable , the displacement grows ...
... analysis explains the behavior of the solution in the immediate vicinity of the equilibrium position . In the case in which the linearized stability analysis predicts the equilib- rium solution is unstable , the displacement grows ...
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 |
Common terms and phrases
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