Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 172
... complex , that is p2 - 4q < 0 , r = −p / 2 ± i√√√4q − p2 / 2 . How is rm interpreted ( for integer m ) when r is complex ? Since m is an integer , it is possible to directly calculate powers of a complex number r = x + iy . For ...
... complex , that is p2 - 4q < 0 , r = −p / 2 ± i√√√4q − p2 / 2 . How is rm interpreted ( for integer m ) when r is complex ? Since m is an integer , it is possible to directly calculate powers of a complex number r = x + iy . For ...
Page 173
... complex roots , ri = + i√4q — p2 2 - - r2 = = p _ \ √ / 4q = p2 ; r2 - 2 = 1 one root is the complex conjugate of the other . Since | r1 | = | r2 | and 01 -02 ( as illustrated in Fig . 41-2 ) , it follows that the solution of the ...
... complex roots , ri = + i√4q — p2 2 - - r2 = = p _ \ √ / 4q = p2 ; r2 - 2 = 1 one root is the complex conjugate of the other . Since | r1 | = | r2 | and 01 -02 ( as illustrated in Fig . 41-2 ) , it follows that the solution of the ...
Page 197
... 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 of the eigenvalue ...
... 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 of the eigenvalue ...
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