Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 260
... velocity . The most common is to measure the velocity u , of each car , u , = dx / dt . With N cars there are N different velocities , each depending on time , u , ( t ) i = 1 , . . . , N. In many situations the number of cars is so ...
... velocity . The most common is to measure the velocity u , of each car , u , = dx / dt . With N cars there are N different velocities , each depending on time , u , ( t ) i = 1 , . . . , N. In many situations the number of cars is so ...
Page 264
... velocity field u ( x , t ) = 15x + 30L 15t + L 57.2 . Suppose a velocity field is given : u ( x , t ) = 30x + 30L 15t + L ( a ) Determine the motion of a car which starts at x = L / 2 at t Why does dx / dt = = 0. [ Hint : ( 30x + 30L ) ...
... velocity field u ( x , t ) = 15x + 30L 15t + L 57.2 . Suppose a velocity field is given : u ( x , t ) = 30x + 30L 15t + L ( a ) Determine the motion of a car which starts at x = L / 2 at t Why does dx / dt = = 0. [ Hint : ( 30x + 30L ) ...
Page 312
... velocity and the rope velocity , just as there are car velocity and density wave velocity for traffic flow problems . In traffic flow problems , there are two important velocities : one the velocity of individual cars and the other the ...
... velocity and the rope velocity , just as there are car velocity and density wave velocity for traffic flow problems . In traffic flow problems , there are two important velocities : one the velocity of individual cars and the other the ...
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