Computer Modeling: From Sports to Spaceflight-- from Order to Chaos |
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Page 72
... iteration ; Newton's method will end with a small and possibly negative stepsize . ( b ) Newton's method may not converge ; if this happens , avoid an infinite loop by iterating only a few times . The number 5 was chosen arbitrarily ...
... iteration ; Newton's method will end with a small and possibly negative stepsize . ( b ) Newton's method may not converge ; if this happens , avoid an infinite loop by iterating only a few times . The number 5 was chosen arbitrarily ...
Page 90
... iteration has not converged for n = N , you can feel confident in asserting that it will not converge . ( You may or may not be correct ; but if unlimited iterations are allowed , then , eventually , round - off errors may put you onto ...
... iteration has not converged for n = N , you can feel confident in asserting that it will not converge . ( You may or may not be correct ; but if unlimited iterations are allowed , then , eventually , round - off errors may put you onto ...
Page 96
... iteration approaches a solution within some limit , say 0.1 , then declare the iteration to have converged to that solution , and color the starting points accordingly . If the iteration diverges , then color the point black . • Declare ...
... iteration approaches a solution within some limit , say 0.1 , then declare the iteration to have converged to that solution , and color the starting points accordingly . If the iteration diverges , then color the point black . • Declare ...
Contents
Lagranges Equations | 1 |
Some Fundamental Concepts in the Solution of Differential Equations | 11 |
One Approach to Solving a System of Ordinary Differential Equations | 19 |
Copyright | |
24 other sections not shown
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altitude angle angular velocity assume axis ball bifurcation bifurcation diagram bounce c₁ calculate chaos chaotic coefficient components consider constant coordinates curve density depends derivatives differential equation drag dt dt dt dy dx dt dy dt dynamical dynamical system Earth energy equations of motion equilibrium Euler's method friction function gravitational horizontal increase initial conditions integration investigate iteration Jupiter length lift force limit cycle M₁ mass moment of inertia Moon moving Newton's method numerical values orbit oscillations parameters period phase-plane diagram pitch plot Poincaré maps predation r₁ radius rotation satellite shown in figure simple pendulum sin² Skylab solution solved spacecraft spin spring stable starting conditions step stepsize Suppose swing TeMax trajectory truncation error unstable variables vary x-axis x-y plane y₁ zero