CSULB MAE 501 Exam 2

CSULB MAE 501 Exam 1

Fractal?

Cli-Fi
(A conversation starring A, B & C)

a. This is a story about change in climate...

b. Really?

a. I thought the climate only changed 4 times a year (seasons)?

b. Yeahhhh... that was the case before. Now it is a little different, today...

a. Wait, isn't climate controlled by the rotation of earth around the sun?

b. Yup, that was the idea back in the day...

a. So, if the year only has 365 days. Then our climate should be constant...

c. Don't forget about the extra day we have each 4 years...

a. Then it changes a little over time... Essentially, yeah just a little...

c. What about our influence on the planet??? Would that change the climate as well?

a. Well... earth is an ecosystem. Ecosystems need certain constants in order to prevail...

b. Soooo... what if we remove all constants...

c. Then, my friend... you remove the ecosystem.

Complex Quantum Cosmos: Science Puzzles and Technology Solutions - M. Sp...

This lecture was a fresh reminder that we are barely in the first stages of a quantum based physics.

Interplanetary Missions

This MATLAB function was created to simulate Hooman transfer in the solar system.

function LunaOcampo_Pedro_Interplanetary(n,z) 

% This function provides the following data for interplanetary missions:

% 1. Total ?v for the Hohmann transfer to and back from the planet

% 2. Total Travel Time

% 3. Synodic Time Period

% 4. Wait time

% 5. Departure characteristics

%    a. Angular momentum, eccentricity of departure hyperbola from a ?z? km altitude circular 

%       parking orbit around earth

%    b. ?v from parking orbit to departure hyperbola

% 6. Arrival characteristics

%    a. Angular momentum, eccentricity of arrival hyperbola to get into an optimal circular 

%       orbit around the planet. If an optimal circular orbit does not exist, use a capture orbit 

%       with altitude ?z?.

%    b. ?v to get into the circular orbit and radius, time period of the capture orbit

%

% The labeling of the planets (n) is as follow:

% 1 Mercury

% 2 Venus

% 3 Earth

% 4 Mars

% 5 Jupiter

% 6 Saturn

% 7 Uranus

% 8 Neptune

%

% z is the altitude of the parking orbit around Earth

clc

n=4;z=650;

if n == 3 

    display(' ')

    error('Earth is not a valid destination!')

end

if n > 3

    n = n-1;

end

rade =  6378; %km

re = 149.6e6 ; %km

r = [57.91e6 108.2e6 227.9e6 778.6e6 1.433e9 2.872e9 4.495e9]; %km

rap = [2440 6052 3396 71490 60270 25560 24760]; %km

SR = 23.9345; %hrs

T1 = 365.256 * SR; %hrs

T2 = [87.97*SR 224.7*SR 1.881*T1 11.86*T1 29.46*T1 84.01*T1 164.8*T1]; %hrs

mu = 132712000000; %km^3/s^2

mup = [22030 324900 42828 126686000 37931000 5794000 6835100]; %km^3/s^2

mue = 398600; %km^3/s^2

dVa = abs(sqrt(2 * (mu / re - mu / (re + r(n)))) - sqrt(mu / re)); %kms/s

dVb = abs(sqrt(2 * (mu / r(n) - mu / (re + r(n)))) - sqrt(mu / r(n))); %kms/s

tdV = 2*(dVa + dVb); %kms/s

Tsyn = T1 * T2(n) / abs(T1 - T2(n)); %hrs

Tsynd = Tsyn / 24 ; %days

n1 = 2 * pi / T1; %rev/hr

n2 = 2 * pi / T2(n);  %rev/hr

a = (re + r(n)) / 2;

t12 = (pi * a^1.5) / sqrt(mu);%sec 

t12 = t12/3600;

t12d = t12/24; %days

phi_f = pi - n1 * t12;

N = 1;

if n1 > n2

    twait = (-2*phi_f - 2 * pi * N) / (n2 - n1);

    while twait <= 0

    twait = (-2*phi_f - 2 * pi * N) / (n2 - n1);

    N = N + 1;

    end

else

    twait = (-2*phi_f + 2 * pi * N) / (n2 - n1);

    while twait <= 0

    twait = -2*phi_f + 2 * pi * N / (n2 - n1);

    N = N + 1;

    end

end

twait = twait/24;

disp(' ')

disp('Interplanetary Trajectory from Earth to Planet')

disp('----------------------------------------------')

disp(' ')

fprintf('Total Delta V for the Hohmann transfer = %4.2f km/s ',tdV)

disp(' ')

fprintf('Total travel time = %4.2f days',t12d)

disp(' ')

fprintf('Synodic Period = %4.2f days',Tsynd)

disp(' ')

fprintf('Wait time = %4.2f days',twait)

disp(' ')

%%% Departure %%%

rc = rade + z;

Vinfd = dVa;

ed = 1 + (rc * Vinfd ^ 2) / mue;

hd = mue * sqrt(ed ^ 2 - 1) / Vinfd;

Vp = hd / rc;

Vc = sqrt(mue/rc);

dVd = abs(Vc - Vp);

disp(' ')

disp('Departure Characteristics')

disp('-------------------------')

disp(' ')

fprintf('Angular momentum of departure hyperbola = %4.2f km2/s2 ',hd)

disp(' ')

fprintf('Eccentricity of departure hyperbola = %4.2f ',ed)

disp(' ')

fprintf('Delta V = %4.2f km/s',dVd)

disp(' ')

%%% Arrival %%%

Vinfa = dVb;

ra = 2 * mup(n) / Vinfa^2; 

if ra < rap(n)

    ra = rap(n) + z;

end

ea = 1 + ra * Vinfa^2 / mup(n);

ha = mup(n) * sqrt(ea^2 - 1) / Vinfa;

Tpc = 2 * pi * ra ^ (1.5) / sqrt(mup(n));

dVaR = abs(sqrt(Vinfa^2 + 2 * mup(n) / ra) - sqrt(mup(n) / ra));

disp(' ')

disp('Arrival Characteristics')

disp('-------------------------')

disp(' ')

fprintf('Angular momentum of arrival hyperbola = %4.2f km2/s2 ',ha)

disp(' ')

fprintf('Eccentricity of arrival hyperbola = %4.2f ',ea)

disp(' ')

fprintf('Radius of optimal capture orbit = %4.2f km ',ra)

disp(' ')

fprintf('Time period of capture orbit = %4.2f km ',Tpc)

disp(' ')

fprintf('Delta V = %4.2f km/s',dVaR)

disp(' ')

end

The Sierpinski triangle implemented in MATLAB

Here is the code used to generate the triangle above:

n = 1000 %input('number of iterations? ')

m=2; xi=zeros(n);yi=zeros(n);

for m = 2:n

    r = randi([1 3]);

    

    switch r

        case 1

            xi(m)=.5*xi(m-1);

            yi(m)=.5*yi(m-1);

        case 2

            xi(m)=.5*xi(m-1)+.25;

            yi(m)=.5*yi(m-1)+sqrt(3)/4;

        case 3

            xi(m)=.5*xi(m-1)+.5;

            yi(m)=.5*yi(m-1);

    end

end

plot(xi,yi,'^')