## How to solve 3 equations dependent each other?

### hknatas (view profile)

on 10 Nov 2018
Latest activity Edited by hknatas

on 11 Nov 2018

### Bruno Luong (view profile)

Hello. How to code this situation?
In this situation i need to calculate all angular velocities from time 0s to time 5400s with increase by 0.1s and graph them.
I have all the initial values:
wxi = 0.0065
wyi = 0.0066
wzi = 0.0067
And constant values:
NT = 3.6 * 10^-10
Jx = 2.1 * 10^-3
Jy = 2.0 * 10^-3
Jz = 1.9 * 10^-3
Actually i thought it is going to be easy but when i write the code for wx, i realized that wx is increasing with time but wz and wy in the equation are constant values. Which kind of loop should i use? Thanks for the answers!

Walter Roberson

### Walter Roberson (view profile)

on 10 Nov 2018
wz(i+1) = wz(i) + delta_t / Jz * (wx(i) * wy(i) + NT)*(Jx - Jy);
hknatas

### hknatas (view profile)

on 10 Nov 2018
Thanks a lot, it really helps. However i guess i should use a few command which i don't know. As i understand it, i should create wx, wy and wz arrays first. My arrays should have 54000 data and all of them should be equal to their initial values at first. Then after equations are executed one time, second data in my array will change to the new wx value. Did i get the idea correctly? Also my initial conditions are not integer so i need to define an array with float numbers. How can i describe such an array then?
hknatas

### hknatas (view profile)

on 10 Nov 2018
In here delta_t = time_vals right? And when i tried to run program an error occurs : "Unable to perform assignment because the left and right sides have a different number of elements." What can be the problem?
This is my whole code:
clc;
clear;
clear all
n = 63
Wx(1) = 0.0002 + 0.0001 * n; % 0.0065
Wy(1) = 0.0003 + 0.0001 * n; %0.0066
Wz(1) = 0.0004 + 0.0001 * n; %0.0067
% The initial moments of inertia of the satellite ( m^4 ):
Jx = 2.1e-03;
Jy = 2e-03;
Jz = 1.9e-03;
% The disturbance torque acting on the satellite ( N.m ):
NT = 3.6e-10;
delta_t = 0:0.1:5400;
N_times = length(delta_t);
for i = 1 : N_times
Wx(i+1) = Wx(i) + delta_t / Jx * (Wz(i) * Wy(i) + NT)*(Jy - Jz);
Wy(i+1) = Wy(i) + delta_t / Jy * (Wx(i) * Wz(i) + NT)*(Jz - Jx);
Wz(i+1) = Wz(i) + delta_t / Jz * (Wx(i) * Wy(i) + NT)*(Jx - Jy);
end

### Bruno Luong (view profile)

on 10 Nov 2018

Actually i thought it is going to be easy but when i write the code for wx, i realized that wx is increasing with time but wz and wy in the equation are constant values.
Just copy the value in 3 different variables, then do the calculation.

hknatas

### hknatas (view profile)

on 11 Nov 2018
I am so grateful, thanks for everthing. One more thing i want to ask: What if i want to Wx as a dependent of time? When i write plot(time_vals,Wx) it says Vectors must be the same length.
Walter Roberson

### Walter Roberson (view profile)

on 11 Nov 2018
delta_t = 0.1;
time_vals = 0 : delta_t : 5400;
N_times = length(time_vals);
n = 63;
Wx = zeros(1, N_times);
Wy = zeros(1, N_times);
Wz = zeros(1, N_times);
Wx(1) = 0.0002 + 0.0001 * n; % 0.0065
Wy(1) = 0.0003 + 0.0001 * n; %0.0066
Wz(1) = 0.0004 + 0.0001 * n; %0.0067
% The initial moments of inertia of the satellite ( m^4 ):
Jx = 2.1e-03;
Jy = 2e-03;
Jz = 1.9e-03;
% The disturbance torque acting on the satellite ( N.m ):
NT = 3.6e-10;
for i = 1 : N_times - 1
Wx(i+1) = Wx(i) + delta_t / Jx * (Wz(i) * Wy(i) + NT)*(Jy - Jz);
Wy(i+1) = Wy(i) + delta_t / Jy * (Wx(i) * Wz(i) + NT)*(Jz - Jx);
Wz(i+1) = Wz(i) + delta_t / Jz * (Wx(i) * Wy(i) + NT)*(Jx - Jy);
end
plot(time_vals, Wx);
hknatas

### hknatas (view profile)

on 11 Nov 2018
Thanks for everything, especially for your patience. This really helps a lot.