Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page vi
... NONLINEAR PENDULUM 23. CAN A PENDULUM STOP ? 82 24. WHAT HAPPENS IF A PENDULUM IS PUSHED TOO HARD ? 84 25. PERIOD OF A NONLINEAR PENDULUM 87 * 76 26. NONLINEAR OSCILLATIONS WITH DAMPING 91 27. EQUILIBRIUM POSITIONS AND LINEARIZED ...
... NONLINEAR PENDULUM 23. CAN A PENDULUM STOP ? 82 24. WHAT HAPPENS IF A PENDULUM IS PUSHED TOO HARD ? 84 25. PERIOD OF A NONLINEAR PENDULUM 87 * 76 26. NONLINEAR OSCILLATIONS WITH DAMPING 91 27. EQUILIBRIUM POSITIONS AND LINEARIZED ...
Page 55
... nonlinear pendulum also satisfies a differential equation of that form , since d20 L dt2 = g sin 0 . ( 17.2 ) Before solving these nonlinear ordinary differential equations , what properties do we expect the solution to have ? For small ...
... nonlinear pendulum also satisfies a differential equation of that form , since d20 L dt2 = g sin 0 . ( 17.2 ) Before solving these nonlinear ordinary differential equations , what properties do we expect the solution to have ? For small ...
Page 111
... pendulum diminishes after each oscillation due to the small friction ( as illustrated in Fig . 28-10 ) . V = d0 dt Figure 28-10 Phase plane if k2 < 4Lg : sketch illustrating ... pendulum 111 Sec . 28 Nonlinear Pendulum with Damping.
... pendulum diminishes after each oscillation due to the small friction ( as illustrated in Fig . 28-10 ) . V = d0 dt Figure 28-10 Phase plane if k2 < 4Lg : sketch illustrating ... pendulum 111 Sec . 28 Nonlinear Pendulum with Damping.
Contents
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
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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