computing a sequence of vectors

the sequence is defined, for i = 1:n, by this vectorial recurrence relation :

[A(i+1); B(i+1)] = Q * [A(i); B(i)] + [C; D]

with Q = [-(L+d)/d, L/d; -L/d, (L-d)/d]

and [C; D] = 0.5 * q * sin(alpha) * [L + d; L^2/d]

Where n, L, d, q, alpha are given constants

I want to compute symbollically [A(i); B(i)] as a function of [A(n); B(n)], which is known.

How to model in matlab the quantities [A(i); B(i)] for i = 1:n ?

Answer 1

[Birdman]

Try the following code:

n=1;L=1;d=1;q=1;%randomly given

syms alpha
C=0.5*q*sin(alpha)*[L+d];
D=0.5*q*sin(alpha)*[L^2/d];
Q=[-(L+d)/d,L/d;-L/d,(L-d)/d];

n=10;%randomly given

A=sym(zeros(n,1));B=sym(zeros(n,1));%preallocation

for i=1:n
    temp=Q*[A(i);B(i)]+[C;D];
    A(i+1)=temp(1);
    B(i+1)=temp(2);
end

Then display the values to see if they are correctly obtained.