Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 49
... called a central force . ( a ) Derive the differential equations governing the angle 0 and the dis- tance L [ Hint : Use the equation for a determined in exercise 14.2b ] . ( b ) Show that L2 ( d0 / dt ) is constant [ Hint ...
... called a central force . ( a ) Derive the differential equations governing the angle 0 and the dis- tance L [ Hint : Use the equation for a determined in exercise 14.2b ] . ( b ) Show that L2 ( d0 / dt ) is constant [ Hint ...
Page 63
... called the potential energy ( relative to the position x = x1 ) . Equation 19.2 is called the equation of conservation of energy or the energy equation . The total energy is shared between kinetic energy and potential energy . For ...
... called the potential energy ( relative to the position x = x1 ) . Equation 19.2 is called the equation of conservation of energy or the energy equation . The total energy is shared between kinetic energy and potential energy . For ...
Page 349
... called the position of the shock . Let both the * A function f ( x ) is said to have a jump - discontinuity at x ... called sound waves . When fluctuations of pressure and density are small , the equations describing sound waves can be ...
... called the position of the shock . Let both the * A function f ( x ) is said to have a jump - discontinuity at x ... called sound waves . When fluctuations of pressure and density are small , the equations describing sound waves can be ...
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 |
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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