Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 191
... methods to solve these equations will be discussed . A. METHOD OF ELIMINATION The first method is straightforward ( 191 Sec . 45 System of Two Constant Coefficient First - Order Differential Equations SYSTEM OF TWO CONSTANT COEFFICIENT ...
... methods to solve these equations will be discussed . A. METHOD OF ELIMINATION The first method is straightforward ( 191 Sec . 45 System of Two Constant Coefficient First - Order Differential Equations SYSTEM OF TWO CONSTANT COEFFICIENT ...
Page 192
... METHOD OF ELIMINATION The first method is straightforward ( but has the disadvantage of frequently being cumbersome with problems involving more than two equations ) . If c0 * , then x can be eliminated from equation 45.1a using ...
... METHOD OF ELIMINATION The first method is straightforward ( but has the disadvantage of frequently being cumbersome with problems involving more than two equations ) . If c0 * , then x can be eliminated from equation 45.1a using ...
Page 193
... METHOD ( USING MATRIX THEORY ) An alternative to the method of elimination is to solve the linear system , equations 45.1a and 45.1b , using the matrix and vector notation : 10 or d X = a b x * [ ] [ I ] dt y c de = A dv dt = Av ...
... METHOD ( USING MATRIX THEORY ) An alternative to the method of elimination is to solve the linear system , equations 45.1a and 45.1b , using the matrix and vector notation : 10 or d X = a b x * [ ] [ I ] dt y c de = A dv dt = Av ...
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