Computer Modeling: From Sports to Spaceflight-- from Order to Chaos |
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Page 178
... angle between the plane of the discus and the velocity , y , called the angle of attack . So this angle must be calculated as the equations are solved . The equations of motion are d2x dt2 pAv ? = ( CD cos ẞ + CL sin ẞ ) , 2m ( 9.15.3 ) ...
... angle between the plane of the discus and the velocity , y , called the angle of attack . So this angle must be calculated as the equations are solved . The equations of motion are d2x dt2 pAv ? = ( CD cos ẞ + CL sin ẞ ) , 2m ( 9.15.3 ) ...
Page 199
... Angle , degrees Roll angle 10- -10 20 Pitch angle- Angle , degrees Roll angle 10 -10 -20 -20 50 100 Time 50 100 Time ( a ) ( b ) Angle , Pitch angle . degrees Roll angle 20 10 -10 -20 0 50 100 ( c ) Angle , degrees Pitch angle . Roll angle ...
... Angle , degrees Roll angle 10- -10 20 Pitch angle- Angle , degrees Roll angle 10 -10 -20 -20 50 100 Time 50 100 Time ( a ) ( b ) Angle , Pitch angle . degrees Roll angle 20 10 -10 -20 0 50 100 ( c ) Angle , degrees Pitch angle . Roll angle ...
Page 276
... angle of incidence i , and angle of refraction i + di . The angles are measured from the line normal to the plane tangent to the media . Let the media . have densities p and p + dp and let the index of refraction be proportional to 1 + ...
... angle of incidence i , and angle of refraction i + di . The angles are measured from the line normal to the plane tangent to the media . Let the media . have densities p and p + dp and let the index of refraction be proportional to 1 + ...
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