Pendulum equations setup help

%setup : t, starts at 0, with time step dt, until tfinal , which is 1000 seconds.
%initialize the x, ? dot, ? double dot, θ, ? dot, and ? double dots and F vectors as zeros, all the same size as t (time). 
%Set the first value of the θ vector to θ0

t=(0,1000,dt);

%any help on this I really appreciate it

Answer 1

[NVSL]

Hey @william Smith

I understand you are trying to initialise few vectors with a pre-defined size. You can do so by using ‘zeros’ function which pre-allocates defined space by initialising the vector with zeroes.

Here's how you can create this setup:

% Time setup
dt = 0.01;           % Time step (seconds)
tfinal = 1000;       % Final time (seconds)
t = 0:dt:tfinal;     % Time vector

% Preallocate variables
x = zeros(size(t));             % Position
x_dot = zeros(size(t));         % Velocity
x_ddot = zeros(size(t));        % Acceleration

theta = zeros(size(t));         % Angle (θ)
theta_dot = zeros(size(t));     % Angular velocity (θ̇)
theta_ddot = zeros(size(t));    % Angular acceleration (θ̈)

F = zeros(size(t));             % Force

% Initial condition
theta0 = deg2rad(10);           % Example: initial angle of 10 degrees
theta(1) = theta0;              % Set first value of theta

You can modify "dt" and "theta0" as needed. The "deg2rad" function is used to convert degrees to radians — this is optional depending on your unit preference.

More details on how to initialise a vector using “zeros” function can be found from the below documentation link:.

https://www.mathworks.com/help/matlab/ref/zeros.html

I hope this is beneficial!