computing a sequence of vectors

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genevois pierre on 31 Dec 2020
Answered: Birdman on 13 Jan 2021
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 ?

Birdman on 13 Jan 2021
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.

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