Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 56
... stability is not a difficult one . Basically , an equilibrium solu- tion of a time - dependent equation is said to be stable if the ( usually time- dependent ) solution stays “ near " the equilibrium solution for all initial conditions ...
... stability is not a difficult one . Basically , an equilibrium solu- tion of a time - dependent equation is said to be stable if the ( usually time- dependent ) solution stays “ near " the equilibrium solution for all initial conditions ...
Page 102
... stable if , for all initial conditions near x = x , and v = 0 , the displacement from equilibrium does not grow ... stable ( i.e. , c > 0 and k > 0 ) . Stable if c > 0 . Unstable if c < 0 . Unstable if c < 0 . Stable if c 0 ( sometimes ...
... stable if , for all initial conditions near x = x , and v = 0 , the displacement from equilibrium does not grow ... stable ( i.e. , c > 0 and k > 0 ) . Stable if c > 0 . Unstable if c < 0 . Unstable if c < 0 . Stable if c 0 ( sometimes ...
Page 201
... STABLE р 0 NEUTRALLY STABLE These results are summarized in Fig . 46-1 . A similar diagram appeared in Sec . 27 referring to the stability of an equilibrium position of a spring - mass system with friction . In this manner we are able ...
... STABLE р 0 NEUTRALLY STABLE These results are summarized in Fig . 46-1 . A similar diagram appeared in Sec . 27 referring to the stability of an equilibrium position of a spring - mass system with friction . In this manner we are able ...
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