Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 69
... phase plane relating x and dx / dt is known , and looks as sketched in Fig . 20-3 . Although x and dx / dt are as yet unknown functions of t , they satisfy a relation indicated by the curve in dx dt ** X Figure 20-3 . the phase plane ...
... phase plane relating x and dx / dt is known , and looks as sketched in Fig . 20-3 . Although x and dx / dt are as yet unknown functions of t , they satisfy a relation indicated by the curve in dx dt ** X Figure 20-3 . the phase plane ...
Page 81
... phase plane , the curve corresponding to E = 2g is that shown in Fig . 22-9 . Thus , we have Fig . 22-10 . Using this last result , the still incomplete phase plane is sketched in Fig . 22-11 . The energy integral enables us to sketch ...
... phase plane , the curve corresponding to E = 2g is that shown in Fig . 22-9 . Thus , we have Fig . 22-10 . Using this last result , the still incomplete phase plane is sketched in Fig . 22-11 . The energy integral enables us to sketch ...
Page 190
... phase plane equation . The method of isoclines may again assist in the sketching of the solution curves . Recall in the study of mechanical vibrations that the most important features of the solution in the phase plane occurred in the ...
... phase plane equation . The method of isoclines may again assist in the sketching of the solution curves . Recall in the study of mechanical vibrations that the most important features of the solution in the phase plane occurred in 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