How to solve parametric system of vector equations?
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I have two parameters: P1 and P2, they are vectors. I am looking for a C vector and r scalar.
I have constraints: (P1-C)^2 == (P2-C)^2 == r^2 ; (C-(P1+P2)/2)*(P1-P2) == 0 ; 1+r^2 == C^2
Now I have tried creating symbolic variables, such as a, b and then P1 = (a,b). But somehow the dot product of two vectors becomes some complex vector.
So the question is, can I solve a system of equations such as this, using vectors?
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Christopher Creutzig
2020-3-25
If you do not say differently, symbolic variables are complex (and scalar). The dot product therefore follows the rules in the complex plane. Please try syms a b real, and if you still run into problems, please post a minimal, but complete code snippet, i.e., something others can copy and run.
采纳的回答
David Goodmanson
2020-3-22
编辑:David Goodmanson
2020-3-22
Hi Daniel,
interesting problem. does this correspond to a particular physical situation?
% P1 --> a, P2 --> b
% solution is for c^2 = r^2 + z^2
a = 2*rand(3,1)-1;
b = 2*rand(3,1)-1;
z = 1; % specific case
p = (a+b)/2;
q = (b-a)/2;
u = cross(p,q); % perpendicular to plane defined by a and b
w = cross(u,q);
w = w/norm(w); % unit vector in ab plane, perpendicular to (b-a)
lambda = (dot(q,q)+z^2-dot(p,p))/(2*dot(p,w));
c = p+lambda*w;
r = sqrt(dot(q,q)+lambda^2);
% checks, should be small
dot(c-a,c-a) - r^2
dot(c-b,c-b) - r^2
dot(c -((a+b)/2),b-a)
dot(c,c) - (r^2+z^2)
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