Trapezium Graphs Plots not Plotting

I'm trying to plot the x and y compoments of an object as the angle between the vertical and the direction of flight inreases from 0 to pi/2. I'm using the trapezium rule, finding the area of each segment to try and plot the speed from the acceleration plot, and also to find the displacement from the speed plot.

But my graphs are only giving me constant values for speed and acceleration as shown below:

Why are the values of speed and displacement not changing?

This is my code:

t_step_size = 1;

t_start = 89; %s

t_end = 3689;

t_x = 89:1:3689;

t_step_tot = (t_end - t_x(1))/t_step_size;

theta_step = 0.5*pi/t_step_tot;

theta = 0:theta_step:pi/2; %theta increases incrementally according to time

theta_nan = nan(size(theta));

%initial_values

y_double_dot = 2*9.81;

a_y = y_double_dot*cos(theta);

a_y_nan = nan(size(a_y));

v_y = 1765.8;

y = 76.461;

x_double_dot = y_double_dot*sin(theta);

x_double_dot_nan = nan(size(x_double_dot));

x_dot(1) = 0;

x(1) = 0;

theta_t = nan(size(t_x)); % <--- preallocate the output array

for i = 1:length(numel(theta_t))-1

theta = 0:theta_step:pi/2;

x_dot = theta_step*(x_double_dot_nan(i+1) + x_double_dot_nan(i))/2; %horizontal speed

x = theta_step*(x_double_dot(i+1) + x_double_dot(i))/2; %horizontal displacement

v_y = theta_step*(a_y_nan(i+1) + a_y_nan(i))/2;

y = theta_step*(v_y(i+1) + v_y(i))/2;

end

subplot (3,2,1)

plot(t_x,x_double_dot)

xlabel('Time s')

ylabel('a_x')

subplot (3,2,3)

plot(t_x,x_dot,'o')

xlabel('Time s')

ylabel('v_x')

subplot (3,2,5)

plot(t_x,x_dot,'o')

xlabel('Time s')

ylabel('x')

subplot (3,2,2)

plot(t_x,a_y)

xlabel('Time s')

ylabel('a_y')

subplot (3,2,4)

plot(t_x,v_y,'o')

xlabel('Time s')

ylabel('v_y')

subplot (3,2,6)

plot(t_x,y,'o')

xlabel('Time s')

ylabel('y')

grid on

[David Hill]

You should do your calculations in time. The change in theta is not directly related to the change in time. It is not hard to calculate theta after each time-step. Integrate with respect to time.

[Asit Rahman]

That doesn't work either. This is my code for time itegration:

for i = 1:length(numel(t_x))-1

x_dot(i) = t_step_size*(x_double_dot_nan(i+1) + x_double_dot_nan(i))/2; %horizontal speed

x(i) = t_step_size*(x_double_dot(i+1) + x_double_dot(i))/2; %horizontal displacement

v_y(i) = t_step_size*(a_y_nan(i+1) + a_y_nan(i))/2;

y(i) = t_step_size*(v_y(i+1) + v_y(i))/2;

end

[David Hill]

I am quite confused. How have you defined your axes? Did you not define your y-axis to be aligned with gravity?

%this shows an example in y-direction only
t_start = 89; 
t_end = 3689;
t=t_start:.1:t_end;
y_initial=100000;
vy_initial=0;
ypp=-2*9.81*ones(size(t));
yp=.1*cumtrapz(ypp)+vy_initial;
y=.1*cumtrapz(yp)+y_initial;
plot(t,ypp,t,yp,t,y)

[Asit Rahman]

This is part of a longer series of codes which define other things (which is how I got the initial values)

Your code seems to give the same result. Velocity and displancement do not change

[David Hill]

Not true, displacement and velocity are changing, acceleration is constant. I did not plot angle.

Answer 1

[Torsten]

x_dot = theta_step*(x_double_dot_nan(i+1) + x_double_dot_nan(i))/2; %horizontal speed

v_y = theta_step*(a_y_nan(i+1) + a_y_nan(i))/2;

Replace the nan-arrays by the correct arrays (x_double_dot_nan by x_double_dot and a_y_nan by a_y).

[Asit Rahman]

Doesn't work, I first used x_double_dot and a_y and it still gave the same result