Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 109
... trajectories could " circle " around the equilibrium position ( that is , the trajectories would be closed curves ) , in which case we say the equilibrium position is neutrally stable ; or ( c ) the trajectories could spiral out from ...
... trajectories could " circle " around the equilibrium position ( that is , the trajectories would be closed curves ) , in which case we say the equilibrium position is neutrally stable ; or ( c ) the trajectories could spiral out from ...
Page 110
... trajectories near the area marked in the figure . Some trajectories on the left must cross the isocline along which dv / d0 = 0 and then curve downward as illustrated by curve a . Others , more to the right , must turn towards the right ...
... trajectories near the area marked in the figure . Some trajectories on the left must cross the isocline along which dv / d0 = 0 and then curve downward as illustrated by curve a . Others , more to the right , must turn towards the right ...
Page 208
... trajectories occur if c2 = O , since then x = c1 ′′ 1 — derit C1 y = c1er . Thus again , t is eliminated easily : - - x y - C C d Although this also represents two trajectories emanating from the origin , these trajectories are tending ...
... trajectories occur if c2 = O , since then x = c1 ′′ 1 — derit C1 y = c1er . Thus again , t is eliminated easily : - - x y - C C d Although this also represents two trajectories emanating from the origin , these trajectories are tending ...
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 |
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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