Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 110
... unstable equilibrium position . In a similar manner we can easily see that there are four trajectories which enter this unstable equilibrium position ( two enter backwards in time ) as illustrated in Fig . 28-9 . In Sec . 47B we will ...
... unstable equilibrium position . In a similar manner we can easily see that there are four trajectories which enter this unstable equilibrium position ( two enter backwards in time ) as illustrated in Fig . 28-9 . In Sec . 47B we will ...
Page 201
... UNSTABLE STABLE Р 0 ALGEBRAICALLY UNSTABLE * A < 0 p > 0 UNSTABLE p < 0 STABLE р 0 NEUTRALLY STABLE These results are summarized in Fig . 46-1 . A similar diagram appeared in Sec . 27 referring to the stability of an equilibrium ...
... UNSTABLE STABLE Р 0 ALGEBRAICALLY UNSTABLE * A < 0 p > 0 UNSTABLE p < 0 STABLE р 0 NEUTRALLY STABLE These results are summarized in Fig . 46-1 . A similar diagram appeared in Sec . 27 referring to the stability of an equilibrium ...
Page 222
... by dt dy = cx + dy dt p = a + d q = ad - bc A = p2 - 4q A = 0 ( p2 = 4g ) Unstable spiral Unstable ( borderline case ) Unstable node Neutrally stable ( borderline case ) Unstable saddle point - Unstable ( borderline case ) - 222 y = 4x.
... by dt dy = cx + dy dt p = a + d q = ad - bc A = p2 - 4q A = 0 ( p2 = 4g ) Unstable spiral Unstable ( borderline case ) Unstable node Neutrally stable ( borderline case ) Unstable saddle point - Unstable ( borderline case ) - 222 y = 4x.
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