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 |
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