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 |
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