Trouble in getting analytic and numeric solution for integrating sine wave

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Bruce Rogers 2021-6-8

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https://ww2.mathworks.cn/matlabcentral/answers/850525-trouble-in-getting-analytic-and-numeric-solution-for-integrating-sine-wave

评论： Bruce Rogers 2021-6-8

Hello everyone,

I'm trying to get coordinates for a robot movement from a sine wave. Now I changed the length of one period and the last and most important plot looks aweful. Does anyone can explain what's wrong in my code? I'm using Matlab R2020b for academic use.

clear;
% Distance
t = 0.05; % Frequency
A = 50;  %Amplitude
x = 0:t:10*pi;
y = A*sin(x);       %It's all good if I leave sin(x), but when I want to change the duration of one period, like 2x
                    %the plot looks like in the picture.
T = (1:length(x))*t;
figure(1)
plot(T,y,'.')
xlabel('time')
ylabel('distance')
%%
vel = gradient(y)./gradient(x);
figure(2)
plot(T,vel,'.')
xlabel('time')
ylabel('velocity')
%%
acc = gradient(vel)./gradient(x);
  
figure(3)
plot(T,acc,'.')
xlabel('time')
ylabel('acceleration')
acc = acc';
%xlswrite('Acceleration.xlsx',acc);
acc = acc';
%%
%velocity Cosinus Figure
v = zeros(1,length(acc));
v(1,1) = A * cos(0);
l_v = 1:length(acc);
for i = 2:length(l_v)
    
    v(i) = ((acc(i)+acc(i-1))/2) * t + v(i-1);
    
end
figure(4)
scatter(T,v,'.')
xlabel('time')
ylabel('velocity')
v = v';
%xlswrite('Velocity.xlsx',v);
v = v';
%%
%distance Sinus Figure
s = zeros(1,length(v));
s(1,1) = sin(0);
for i = 2:length(acc)
    
    s(i) = ((v(i)+v(i-1))/2) * t + s(i-1);
    
end
figure(5)
scatter(T,s,'.')
xlabel('time')
ylabel('distance')
s = s';
%xlswrite('idealwaves.xlsx',s)