Computer Modeling: From Sports to Spaceflight-- from Order to Chaos |
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Page 94
... Suppose that we want to find solutions of f ( x , y ) = 0 , and g ( x , y ) = 0 . Starting with some estimate ( xo ... Suppose equations ( 5.5.23 ) have several solutions . For a given starting value ( xo , yo ) which of these solutions ...
... Suppose that we want to find solutions of f ( x , y ) = 0 , and g ( x , y ) = 0 . Starting with some estimate ( xo ... Suppose equations ( 5.5.23 ) have several solutions . For a given starting value ( xo , yo ) which of these solutions ...
Page 341
... Suppose that tstart and start are the values of t and x at the start of the stretch ; then the values of the variables at the end of the stretch are dx t = tstart ( A- Xstart ) / v , x = A , = v . dt After these values are found , fly ...
... Suppose that tstart and start are the values of t and x at the start of the stretch ; then the values of the variables at the end of the stretch are dx t = tstart ( A- Xstart ) / v , x = A , = v . dt After these values are found , fly ...
Page 372
... Suppose the field is defined by 0 ≤ x ≤ A and 0 ≤ y ≤ B. Suppose that the pig's position is currently found from x = xo + at , yp = yo + ẞt . Before taking an integration step , starting at Xp time t , with stepsize h , check to see ...
... Suppose the field is defined by 0 ≤ x ≤ A and 0 ≤ y ≤ B. Suppose that the pig's position is currently found from x = xo + at , yp = yo + ẞt . Before taking an integration step , starting at Xp time t , with stepsize h , check to see ...
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 | |
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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