978-0078112829 Chapter 1 Solution Manual Part 3

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1

Problem 1.19 Numerically solve the differential equation

&&&

y3&&

y4&

y12yte2t

for y at t = 3 if, at t =

0,

y&

y&&

y0

.

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1

Problem 1.20 Numerically solve the differential equation

t&&

yt2&

y2y0

to obtain y at t = 4 if the

initial conditions are y = 0 and

&

y1

at t = 1.

end %problem_1_20

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1

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Problem 1.21 Numerically solve the system

&

xy

2z

20

x

2&

yz

20

x

2y

2&

z0

to obtain x, y and z at t = 20. The initial conditions are x = 1 and y = z = 0 at t = 0.

Solution

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Problem 1.22 Use one of the numerical methods discussed in Section 1.8 to solve Equation 1.127

&&

xg0RE

2

x20

(1)

for the time required for the moon to fall to the earth if it were somehow stopped in its orbit while the

earth remained fixed in space. Compare your answer with the analytical solution,

tr

0

2g0RE

2



4r

0r r

0r

 r

0

2sin 1r

02r

r

0























(2)

Solution

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1

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Problem 1.23 Use a Runge-Kutta solver to solve the nonlinear Lorenz equations

&

x



yx

 

&

yx



z

 y

&

zxy 



z

Use



10

,



8 3

and



28

and the initial conditions x = 0, y = 1 and z = 0 at t = 0. Let t range to a

value of 20 or higher. Plot the phase trajectory x = x(t), y= y(t), z = z(t).

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1