integration using set of matrix equation

if I have the accelartion

and I would like to calculate the theta and its derivative angles

L=1.6; n=16; l=0.1; m=0.1; I=0.0001 g=9.8; kn=2;
alpha=pi/6; mu=0.3; a=0.0625; T=32;
xl_0=0; zl_0=0; xD1_0=0;  zD1_0=0;  pD1_0=0;  G=m*n*g;

theta(1:n-1)=-2*alpha*sin(kn*pi/n)*sin(2*kn*pi*s/L+2*kn*pi*(1:n-1)/n+kn*pi/n);
thetaD(1:n-1)=(-4*kn*pi*alpha/L)*sin(kn*pi/n)*cos(2*kn*pi*s/L+2*kn*pi*(1:n-1)/n+kn*pi/n)*sd;

phi(1:n)=alpha;
phi(2:n)=phi(1:n-1)+theta(1:n-1);

how can calculate them

can anyone help me please?

Answer 1

[Walter Roberson]

In https://www.mathworks.com/matlabcentral/answers/506724-how-to-solve-this-equation-for-laplace-transform-with-matlab#comment_802772 I show how to use heaviside() to implement piecewise calculations in a way that can be integrated (or fourier transformed, or laplace transformed.) See in particular the helper function I named R. The first parameter is the variable name; the second parameter is the lower bound that applies; the third parameter is the upper bound that applies; the last parameter is the value that is to apply inside that range.

[areej abdulshaheed]

I couldn't unserdatnd anything

can you re_write on the program I sent? please.

[Walter Roberson]

None of the variables you have in your code appear to have anything to do with the equation you posted, except that possibly your T = 32 corresponds to the T that is used in the equation.

Is alpha intended to be the same as the a in your equations? The a in your equations is acceleration, which is seldom represented by using α .

Calculating theta and its derivative angles does not appear to have anything to do with ?

Is s here the same s that would be written in a laplace transform of a continuous time system? But if so then you would not talk about taking the drivative of such a system: in laplace transform, additional derivatives correspond to multiplying by s. You might, I suppose, talk about being a particular value...

[areej abdulshaheed]

it is the- s- in theta equation

sin(2*kn*pi*s/L+2*kn*pi*(1:n-1)/n+kn*pi/n);

[Walter Roberson]

Is the same as the s in that equation, or is the the second derivative of the s in that equation?

The is effectively a function of t but in the equation for theta you are treating s as a variable. I do not see any t in the theta equation ? Is the idea that at each different angle, you would want a different time-based formula ?