Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 68
... curve in the dx / dt vs. x space , for each value of E : dx dt X Figure 20-1 Typical energy curve . For each time , the solution x ( t ) corresponds to one point on this curve since if x ( t ) is known so is dx / dt . As time changes ...
... curve in the dx / dt vs. x space , for each value of E : dx dt X Figure 20-1 Typical energy curve . For each time , the solution x ( t ) corresponds to one point on this curve since if x ( t ) is known so is dx / dt . As time changes ...
Page 69
... curve is quite significant because we can determine certain qualitative features of the solution directly from it . For example for the curve in Fig . 20-3 , since the solution is in the upper half plane , dx / dt > 0 , it follows that ...
... curve is quite significant because we can determine certain qualitative features of the solution directly from it . For example for the curve in Fig . 20-3 , since the solution is in the upper half plane , dx / dt > 0 , it follows that ...
Page 232
... curve is spiralling inwards ( as though the populations of fish and sharks after an oscillation approach closer to their equilibrium values ) , and also part of another solution curve is spiralling outwards ( as though the fish and ...
... curve is spiralling inwards ( as though the populations of fish and sharks after an oscillation approach closer to their equilibrium values ) , and also part of another solution curve is spiralling outwards ( as though the fish and ...
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 |
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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