Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 17
... units of feet , inches , miles , meters , or smoots . * In any calculation to eliminate possible confusion only one unit of length should be used . In this text we will use metric units in the m - k - s system , i.e. , meters for length ...
... units of feet , inches , miles , meters , or smoots . * In any calculation to eliminate possible confusion only one unit of length should be used . In this text we will use metric units in the m - k - s system , i.e. , meters for length ...
Page 44
... unit vectors which not only have fixed magnitude but also have fixed directions . ) In polar coordinates ( centered at the fixed vertex of the pendulum ) , the position vector is pointed outward with length L , = Lî , ( 14.1 ) where is ...
... unit vectors which not only have fixed magnitude but also have fixed directions . ) In polar coordinates ( centered at the fixed vertex of the pendulum ) , the position vector is pointed outward with length L , = Lî , ( 14.1 ) where is ...
Page 276
... unit time crossing at x = a ( moving to the right ) minus the number of cars per unit time crossing ( again moving to the right ) at x = b , or = dN dt = q ( a , t ) — q ( b , t ) , ( 60.2 ) since the number of cars per unit time is the ...
... unit time crossing at x = a ( moving to the right ) minus the number of cars per unit time crossing ( again moving to the right ) at x = b , or = dN dt = q ( a , t ) — q ( b , t ) , ( 60.2 ) since the number of cars per unit time is the ...
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