Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 282
... equation , conservation of cars , ар a of + 2 + ( pu ) 3+ ( pu ) = 0 . ( 61.1 ) If the velocity field is known , equation 61.1 reduces to a partial differential ... ordinary differential equation for the position of a mass or the ordinary ...
... equation , conservation of cars , ар a of + 2 + ( pu ) 3+ ( pu ) = 0 . ( 61.1 ) If the velocity field is known , equation 61.1 reduces to a partial differential ... ordinary differential equation for the position of a mass or the ordinary ...
Page 299
... equation is an initial condition . With an nth order ordinary differential equation , n initial conditions are needed . The number of conditions are correspondingly the same for partial differential equations . Thus for equation 65.3 ...
... equation is an initial condition . With an nth order ordinary differential equation , n initial conditions are needed . The number of conditions are correspondingly the same for partial differential equations . Thus for equation 65.3 ...
Page 399
... equation ) Lincoln Tunnel , 286-293 , 298 , 322 , 326 Linear algebra , 140-141 Linear damping force , 30 Linear oscillator , phase plane , 70-75 Linear partial differential equations , 303- 308 Linearization , 156-158 , 168-169 , 189 ...
... equation ) Lincoln Tunnel , 286-293 , 298 , 322 , 326 Linear algebra , 140-141 Linear damping force , 30 Linear oscillator , phase plane , 70-75 Linear partial differential equations , 303- 308 Linearization , 156-158 , 168-169 , 189 ...
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