Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 280
... conservation of cars . ( 2 ) The equation of conservation of cars can be derived more expedi- tiously . Consider the intergral conservation law , equation 60.4a , for any finite segment of highway , a < x < b . Now take the partial ...
... conservation of cars . ( 2 ) The equation of conservation of cars can be derived more expedi- tiously . Consider the intergral conservation law , equation 60.4a , for any finite segment of highway , a < x < b . Now take the partial ...
Page 385
... conservation of cars . The rate of change of cars between x x = x1 and x = = Figure 83-1 Exits and entrances . x1 and x = x2 results not only from cars crossing at x2 , but also from cars entering or exiting the road between x = x1 and ...
... conservation of cars . The rate of change of cars between x x = x1 and x = = Figure 83-1 Exits and entrances . x1 and x = x2 results not only from cars crossing at x2 , but also from cars entering or exiting the road between x = x1 and ...
Page 396
... Conservation law ( see also Conservation of angular momentum ; Conserva- tion of cars ; Conservation of energy ) differential , 347-348 integral , 277 , 347-348 local , 278 Conservation of angular momentum , 49 Conservation of cars ...
... Conservation law ( see also Conservation of angular momentum ; Conserva- tion of cars ; Conservation of energy ) differential , 347-348 integral , 277 , 347-348 local , 278 Conservation of angular momentum , 49 Conservation of cars ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero