Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
From inside the book
Results 1-3 of 88
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
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
Copyright | |
72 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 of oscillation analyze approximation Assume birth c₁ calculation characteristics Consider constant coefficient corresponding d2x dt2 damping de/dt decreases delay depend derived determine difference equation discussed dx dt dx/dt energy integral equilibrium population equilibrium solution equivalent example exercise exponential Figure formula function growth rate Hint increases initial conditions initial value problem isoclines linearized stability analysis logistic equation mass mathematical model maximum method of characteristics motion moving N₁ Newton's nonlinear pendulum number of cars obtained occur ordinary differential equations oscillation P₁ partial differential equation period phase plane Pmax population growth potential energy r₁ result sharks shock Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solution curves solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow trajectories Umax unstable equilibrium position variables vector x₁ yields zero