Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
From inside the book
Results 1-3 of 43
Page 149
... valid for all finite values of j ? = Let us prove our proposed formula , equation 36.7 , by induction . We have already verified this is valid for j 1 , 2. Let us assume it is valid for all j≤jo . If we know all of these probabilities ...
... valid for all finite values of j ? = Let us prove our proposed formula , equation 36.7 , by induction . We have already verified this is valid for j 1 , 2. Let us assume it is valid for all j≤jo . If we know all of these probabilities ...
Page 280
... valid everywhere ( all x ) and for all time . It is called the equation of conservation of cars . ( 2 ) The equation of conservation of cars can be derived more expedi- tiously . Consider the intergral conservation law , equation 60.4a ...
... valid everywhere ( all x ) and for all time . It is called the equation of conservation of cars . ( 2 ) The equation of conservation of cars can be derived more expedi- tiously . Consider the intergral conservation law , equation 60.4a ...
Page 351
... valid elsewhere . However , we have not yet explained where shocks occur and how to determine p1 and p2 . In the next P1 section a calculation of this kind will be undertaken . The shock condition can be derived in an alternate manner ...
... valid elsewhere . However , we have not yet explained where shocks occur and how to determine p1 and p2 . In the next P1 section a calculation of this kind will be undertaken . The shock condition can be derived in an alternate manner ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
80 other sections not shown
Other editions - View all
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