## Computer modeling: from sports to spaceflight-- from order to chaos |

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Page 219

The second describes the

relates the size of an

Newton formulated his law of gravitation to generalize these laws and to apply

them ...

The second describes the

**orbital**speeds at different parts of the**orbit**. The thirdrelates the size of an

**orbit**to the period of revolution. One hundred years later,Newton formulated his law of gravitation to generalize these laws and to apply

them ...

Page 235

You will find the

values suggested, 7.86 to 7.90 will result in just a few revolutions. A value less

than 7.5 could result in the satellite dropping to Earth due to gravity, not drag. A

value ...

You will find the

**orbit**is highly sensitive to the initial speed. With the numericalvalues suggested, 7.86 to 7.90 will result in just a few revolutions. A value less

than 7.5 could result in the satellite dropping to Earth due to gravity, not drag. A

value ...

Page 253

You will need to start with forward thrust, resulting in an

outward. Then if you were to turn off the engine, you would not be moving at right

angles to the radius, so you would not be moving in a circular

...

You will need to start with forward thrust, resulting in an

**orbit**that is spirallingoutward. Then if you were to turn off the engine, you would not be moving at right

angles to the radius, so you would not be moving in a circular

**orbit**. Consequently...

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### Contents

Some Fundamental Concepts in the Solution of Differential Equations | 11 |

Springs | 13 |

One Approach to Solving a System of Ordinary Differential Equations | 19 |

Copyright | |

22 other sections not shown

### Common terms and phrases

altitude angle angular angular velocity approximation assume attractor axis ball bifurcation bifurcation diagram bounce calculation center of mass chaos chaotic comet components conﬁrm consider constant coordinates cricket ball curve deﬁned density depends diagram differential equations dynamical system Earth energy equilibrium Euler’s method ﬁeld Figure ﬁnal ﬁnd ﬁrst ﬁrst-order ﬁxed point ﬂight function gravitational horizontal illustrated in ﬁgure increase initial conditions initial speed integration investigate iteration Jupiter lift force limit cycle Lorenz equations mass Moon moving Newton’s method numerical values orbit oscillations parameters pendulum periodic phase-plane pitch plane plot Poincaré maps population predation radius rocket rotation satellite shown in ﬁgure Skylab solution solved spacecraft spin stable starting conditions step stepsize subroutine Suppose swing TeMax trajectory truncation error variables vary velocity vertical yo-yo zero