Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 141
... tion to this system of difference equations in the form Ñm = rmề , where is a constant vector and where r will be determined . Show that ( A − rI ) C = ō , - where I is the identity matrix . From linear algebra , we know that for ...
... tion to this system of difference equations in the form Ñm = rmề , where is a constant vector and where r will be determined . Show that ( A − rI ) C = ō , - where I is the identity matrix . From linear algebra , we know that for ...
Page 164
... tion would continue to grow at the rate for a population not near equilibrium N ( t ) t Figure 40-2 Delayed growth . ( if t¿ is sufficiently large ) . In this way , the population could go beyond its equilibrium value . Furthermore if ...
... tion would continue to grow at the rate for a population not near equilibrium N ( t ) t Figure 40-2 Delayed growth . ( if t¿ is sufficiently large ) . In this way , the population could go beyond its equilibrium value . Furthermore if ...
Page 180
... tion . N , ( t ) | X X X X X X X t = mat X Figure 42-2 Growing oscillation for large delays ( α > 1 ) . Note in both cases ( 1 ) and ( 2 ) , that , for example , if the displacement popula- tion is greater than 0 , it can increase only ...
... tion . N , ( t ) | X X X X X X X t = mat X Figure 42-2 Growing oscillation for large delays ( α > 1 ) . Note in both cases ( 1 ) and ( 2 ) , that , for example , if the displacement popula- tion is greater than 0 , it can increase only ...
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