Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 141
... obtained by a method similar to that developed in Sec . 33 . ( a ) Use the notation Ñ Ñ ( mAt ) , and hence Nm + 1 = AÑm . Try a solu- Ñ „ = Ñm + 1 tion to this system of difference equations in the form Ñm = rmề , where is a constant ...
... obtained by a method similar to that developed in Sec . 33 . ( a ) Use the notation Ñ Ñ ( mAt ) , and hence Nm + 1 = AÑm . Try a solu- Ñ „ = Ñm + 1 tion to this system of difference equations in the form Ñm = rmề , where is a constant ...
Page 286
... obtained by two observers ( with a machine's assistance ) a short distance apart , as is shown in Fig . 62-2 . The velocity of each vehicle was obtained by recording the times at which they passed each observer ( v = d / ( t2 — t1 ) ...
... obtained by two observers ( with a machine's assistance ) a short distance apart , as is shown in Fig . 62-2 . The velocity of each vehicle was obtained by recording the times at which they passed each observer ( v = d / ( t2 — t1 ) ...
Page 373
... obtained using the shock condition : - = dxsr [ q ] dt [ p ] - Pou ( po ) Po = u ( po ) . ( 82.2 ) As we know , this shock wave travels at the same velocity as each car ( of density po ) . Thus if the light stayed red forever , then we ...
... obtained using the shock condition : - = dxsr [ q ] dt [ p ] - Pou ( po ) Po = u ( po ) . ( 82.2 ) As we know , this shock wave travels at the same velocity as each car ( of density po ) . Thus if the light stayed red forever , then we ...
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