Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 68
... corresponds to one point on this curve since if x ( t ) is known so is dx / dt . As time changes , the point corresponding to the solution changes , sketching a curve in the dx / dt vs. x space . Along this curve energy is conserved ...
... corresponds to one point on this curve since if x ( t ) is known so is dx / dt . As time changes , the point corresponding to the solution changes , sketching a curve in the dx / dt vs. x space . Along this curve energy is conserved ...
Page 197
... corresponding to a complex eigenvalue often has complex entries . To find the eigenvector corresponding to r = 1 i , we can do a similar calculation . However , we note from equation 45.15 that since r = 1 + i is the complex conjugate ...
... corresponding to a complex eigenvalue often has complex entries . To find the eigenvector corresponding to r = 1 i , we can do a similar calculation . However , we note from equation 45.15 that since r = 1 + i is the complex conjugate ...
Page 358
... corresponding to po , ( 3 ) car velocity corresponding to Po ; and ( 4 ) shock velocity between the uniform flow p 。 and bumper - to - bumper traffic Pmax . The resulting space - time diagram is Fig . 78-8 ( in which , as discussed ...
... corresponding to po , ( 3 ) car velocity corresponding to Po ; and ( 4 ) shock velocity between the uniform flow p 。 and bumper - to - bumper traffic Pmax . The resulting space - time diagram is Fig . 78-8 ( in which , as discussed ...
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