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Please help me the Matlab questions!!Attached file is the requirement!!Thank you very much!!!

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HW for MATLAB

Please submit your homework on Canvas by October 11, 2020.

1. Write down the MATLAB commands for each of the following tasks.

(a) Evaluate

101 2

X

i

2π(i − 1)

sin

.

2π

100

i=1

(Hint: sum)

(b) Construct a 50 × 50 matrix, A, and fill in even numbers from 2 to

5000 column-wise, i.e. the first column is 2, 4, 6, 8, · · ·, the second

is 102, 104, 106, 108, · · ·, and so on. (Hint: reshape)

(c) Create a new matrix B containing the even rows and the odd columns

of A.

(d) Construct the following matrix

1 −1 0

−1 2 −1

0 −1 3

C=

..

.

0 ··· 0

0 ··· ···

···

0

−1

..

.

−1

0

···

···

0

..

.

0

0

···

.

119 −1

−1 120

(Hint: diag)

(Note: You need to submit the m-file containing all the MATLAB commands for the above tasks.)

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2. The following differential equations describe the motion of a spaceship in

orbit about the earth (located at the origin) and the moon located at (1,0).

The derivatives are respect to time:

x00

y 00

µ0 (x + µ) µ(x − µ0 )

−

− f x0 ,

r13

r23

µ0 y µy

= −2×0 + y − 3 − 3 − f y 0 ,

r1

r2

=

2y 0 + x −

with

µ=

p

p

1

, µ0 = 1 − µ , r1 = (x + µ)2 + y 2 , r2 = (x − µ0 )2 + y 2 .

82.45

(a) By plotting the orbit y(t) versus x(t) with initial conditions

x(0) = 1.2 , x0 (0) = 0 , y(0) = 0 , y 0 (0) = −1.04935751 ,

show that when f = 0, the orbit is periodic with the period T =

6.19216933. You may use the MATLAB function ode45 to solve the

ODE numerically.

(b) With the same initial conditions as in (a), but with f = 1, solve the

differential equations from t = 0. Plot the orbit to show that the

spaceship eventually crashes.

(c) Repeat the computation of (b) with f = 0.1. Can you guess what is

happening?

(Note: You need to submit the m-files for producing the plots in (a),

(b) and (c) and the image files of the plots. Also, please provide the

description of what happens to the spaceship that you can see from the

plot of (c).)

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Tags:

MATLAB commands

matrix B

even rows

M file

odd columns

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