Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 278
... integral conservation law , equation 60.3 , will be expressed as a local conservation law , valid at each position of the roadway . We will do so in three equivalent ways . * In all three , the endpoints of the segment of the roadway ...
... integral conservation law , equation 60.3 , will be expressed as a local conservation law , valid at each position of the roadway . We will do so in three equivalent ways . * In all three , the endpoints of the segment of the roadway ...
Page 280
... integral . The only function whose integral is zero for all intervals is the zero function . Hence , again equation 60.5 follows . By three equivalent methods , we have shown that др at да = + ax 0 ( 60.7 ) must be valid if there are no ...
... integral . The only function whose integral is zero for all intervals is the zero function . Hence , again equation 60.5 follows . By three equivalent methods , we have shown that др at да = + ax 0 ( 60.7 ) must be valid if there are no ...
Page 351
... integral whose integrand is discon- tinuous . It is best to divide the integral into two parts , X2 X2 S ** p dx = 5 * p dx + S ** p dx . x1 x1 Xs In each integral , the integrand p is continuous and hence we can differentiate each ...
... integral whose integrand is discon- tinuous . It is best to divide the integral into two parts , X2 X2 S ** p dx = 5 * p dx + S ** p dx . x1 x1 Xs In each integral , the integrand p is continuous and hence we can differentiate each ...
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