Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 69
... increases as t increases . Arrows are added to the phase plane diagram to indicate the direction the solution changes with time . In the phase plane shown in Fig . 20-4 , since x increases , the solution x ( t ) moves to the right as ...
... increases as t increases . Arrows are added to the phase plane diagram to indicate the direction the solution changes with time . In the phase plane shown in Fig . 20-4 , since x increases , the solution x ( t ) moves to the right as ...
Page 152
... increases . In some manner , still being investigated by researchers , the increase in density causes the birth rate to decrease , the death rate to increase , or both . At some popula- tion , the birth rate equals the death rate and ...
... increases . In some manner , still being investigated by researchers , the increase in density causes the birth rate to decrease , the death rate to increase , or both . At some popula- tion , the birth rate equals the death rate and ...
Page 218
... increases , r increases ; see Fig . 47-13 . If a / b > 0 , then as increases , r decreases as shown in Fig . 47-14 . The time - dependent equations determine the temporal evolution of the solution . For example at x = 0 , dx / dt + by ...
... increases , r increases ; see Fig . 47-13 . If a / b > 0 , then as increases , r decreases as shown in Fig . 47-14 . The time - dependent equations determine the temporal evolution of the solution . For example at x = 0 , dx / dt + by ...
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