kp_v_out_c =
Collecting terms in a big equation
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I have this big equation bellow, I know that there are some terms that could be grouped to show it in a smaller form.
For example, the denominator could be presented in the form of ((R*(D-1)^2-r_L)^2+L^2*w_v^2))*R*v_i*(ki_i^2 + kp_i^2*w_v^2) instead of v_i*D^4*R^3*ki_i^2 + v_i*D^4*R^3*kp_i^2*w_v^2 - 4*v_i*D^3*R^3*ki_i^2 - 4*v_i*D^3*R^3*kp_i^2*w_v^2 + 6*v_i*D^2*R^3*ki_i^2 + 6*v_i*D^2*R^3*kp_i^2*w_v^2 - 2*v_i*D^2*R^2*ki_i^2*r_L - 2*v_i*D^2*R^2*kp_i^2*r_L*w_v^2 - 4*v_i*D*R^3*ki_i^2 - 4*v_i*D*R^3*kp_i^2*w_v^2 + 4*v_i*D*R^2*ki_i^2*r_L + 4*v_i*D*R^2*kp_i^2*r_L*w_v^2 + v_i*L^2*R*ki_i^2*w_v^2 + v_i*L^2*R*kp_i^2*w_v^4 + v_i*R^3*ki_i^2 + v_i*R^3*kp_i^2*w_v^2 - 2*v_i*R^2*ki_i^2*r_L - 2*v_i*R^2*kp_i^2*r_L*w_v^2 + v_i*R*ki_i^2*r_L^2 + v_i*R*kp_i^2*r_L^2*w_v^2
I tried using collect, but it seems it does not work with expressions, for example:
collect(kp_v_out_c,ki_i^2 + kp_i^2*w_v^2)
Can anyone help me?
syms C D ki_i kp_i L phi_v R r_L v_i w_v
kp_v_out_c = ((w_v^4*(C*D^4*L*R^3*kp_i - 4*C*D^3*L*R^3*kp_i - C*ki_i*D^2*L^2*R^2 ...
+ D^2*L^2*R*kp_i + 6*C*D^2*L*R^3*kp_i + C*r_L*D^2*L*R^2*kp_i + 2*C*ki_i*D*L^2*R^2 ...
- 2*D*L^2*R*kp_i - 4*C*D*L*R^3*kp_i - C*v_i*D*L*R^2*kp_i^2 - 2*C*r_L*D*L*R^2*kp_i ...
- C*ki_i*L^2*R^2 + L^2*R*kp_i - C*ki_i*r_L*L^2*R + r_L*L^2*kp_i + C*L*R^3*kp_i ...
+ C*v_i*L*R^2*kp_i^2 + C*r_L*L*R^2*kp_i) + w_v^2*(6*D^5*R^3*kp_i - D^6*R^3*kp_i ...
+ C*D^4*R^3*ki_i*r_L - 15*D^4*R^3*kp_i + 2*L*D^4*R^2*ki_i - D^4*R^2*kp_i*r_L ...
- 4*C*D^3*R^3*ki_i*r_L + 20*D^3*R^3*kp_i - 8*L*D^3*R^2*ki_i + 2*v_i*D^3*R^2*kp_i^2 ...
+ 4*D^3*R^2*kp_i*r_L + 6*C*D^2*R^3*ki_i*r_L - 15*D^2*R^3*kp_i + 12*L*D^2*R^2*ki_i ...
- 6*v_i*D^2*R^2*kp_i^2 - 6*D^2*R^2*kp_i*r_L + 2*L*D^2*R*ki_i*r_L + D^2*R*kp_i*r_L^2 ...
- 4*C*D*R^3*ki_i*r_L + 6*D*R^3*kp_i - C*L*v_i*D*R^2*ki_i^2 - 8*L*D*R^2*ki_i ...
+ 6*v_i*D*R^2*kp_i^2 + 4*D*R^2*kp_i*r_L - 4*L*D*R*ki_i*r_L - 2*v_i*D*R*kp_i^2*r_L ...
- 2*D*R*kp_i*r_L^2 + C*R^3*ki_i*r_L - R^3*kp_i + C*L*v_i*R^2*ki_i^2 + 2*L*R^2*ki_i ...
- 2*v_i*R^2*kp_i^2 - R^2*kp_i*r_L - C*R*ki_i*r_L^3 + 2*L*R*ki_i*r_L ...
+ 2*v_i*R*kp_i^2*r_L + R*kp_i*r_L^2 + kp_i*r_L^3) - 2*R^2*ki_i^2*v_i ...
+ 2*R*ki_i^2*r_L*v_i + 6*D*R^2*ki_i^2*v_i - 6*D^2*R^2*ki_i^2*v_i ...
+ 2*D^3*R^2*ki_i^2*v_i - 2*D*R*ki_i^2*r_L*v_i)/((L^2*R*kp_i^2*v_i)*w_v^4 ...
+ (v_i*D^4*R^3*kp_i^2 - 4*v_i*D^3*R^3*kp_i^2 + 6*v_i*D^2*R^3*kp_i^2 ...
- 2*v_i*D^2*R^2*kp_i^2*r_L - 4*v_i*D*R^3*kp_i^2 + 4*v_i*D*R^2*kp_i^2*r_L ...
+ v_i*L^2*R*ki_i^2 + v_i*R^3*kp_i^2 - 2*v_i*R^2*kp_i^2*r_L ...
+ v_i*R*kp_i^2*r_L^2)*w_v^2 + v_i*D^4*R^3*ki_i^2 - 4*v_i*D^3*R^3*ki_i^2 ...
+ 6*v_i*D^2*R^3*ki_i^2 - 2*v_i*D^2*R^2*ki_i^2*r_L - 4*v_i*D*R^3*ki_i^2 ...
+ 4*v_i*D*R^2*ki_i^2*r_L + v_i*R^3*ki_i^2 - 2*v_i*R^2*ki_i^2*r_L ...
+ v_i*R*ki_i^2*r_L^2))*cos(phi_v) + (-((C*L^2*R^2*kp_i - 2*C*L^2*R^2*kp_i*D ...
+ C*L^2*R*kp_i*r_L + C*L^2*R^2*kp_i*D^2)*w_v^5 + (L^2*R*ki_i - 2*L*R^2*kp_i ...
+ L^2*ki_i*r_L + C*L*R^3*ki_i + C*R*kp_i*r_L^3 - C*R^3*kp_i*r_L ...
- 2*L*R*kp_i^2*v_i - 2*L^2*R*ki_i*D + 8*L*R^2*kp_i*D - C*R^3*kp_i^2*v_i ...
- 2*L*R*kp_i*r_L + L^2*R*ki_i*D^2 - 12*L*R^2*kp_i*D^2 + 8*L*R^2*kp_i*D^3 ...
- 2*L*R^2*kp_i*D^4 + C*R^2*kp_i^2*r_L*v_i + 6*C*L*R^3*ki_i*D^2 ...
- 4*C*L*R^3*ki_i*D^3 + C*L*R^3*ki_i*D^4 - 6*C*R^3*kp_i*r_L*D^2 ...
+ 4*C*R^3*kp_i*r_L*D^3 - C*R^3*kp_i*r_L*D^4 + 3*C*R^3*kp_i^2*v_i*D ...
+ C*L*R^2*ki_i*r_L + 4*L*R*kp_i*r_L*D - 3*C*R^3*kp_i^2*v_i*D^2 ...
+ C*R^3*kp_i^2*v_i*D^3 - 4*C*L*R^3*ki_i*D + 4*C*R^3*kp_i*r_L*D ...
- 2*L*R*kp_i*r_L*D^2 + 2*L*R*kp_i^2*v_i*D - 2*C*L*R^2*ki_i*r_L*D ...
+ C*L*R^2*ki_i*r_L*D^2 - C*R^2*kp_i^2*r_L*v_i*D)*w_v^3 + (ki_i*r_L^3 ...
- R^3*ki_i + 6*R^3*ki_i*D - 15*R^3*ki_i*D^2 + 20*R^3*ki_i*D^3 - 15*R^3*ki_i*D^4 ...
+ 6*R^3*ki_i*D^5 - R^3*ki_i*D^6 + R*ki_i*r_L^2 - R^2*ki_i*r_L + R*ki_i*r_L^2*D^2 ...
- 6*R^2*ki_i*r_L*D^2 + 4*R^2*ki_i*r_L*D^3 - R^2*ki_i*r_L*D^4 - 2*L*R*ki_i^2*v_i ...
- C*R^3*ki_i^2*v_i - 2*R*ki_i*r_L^2*D + 4*R^2*ki_i*r_L*D + C*R^2*ki_i^2*r_L*v_i ...
+ 3*C*R^3*ki_i^2*v_i*D - 3*C*R^3*ki_i^2*v_i*D^2 + C*R^3*ki_i^2*v_i*D^3 ...
+ 2*L*R*ki_i^2*v_i*D - C*R^2*ki_i^2*r_L*v_i*D)*w_v)/((L^2*R*kp_i^2*v_i)*w_v^4 ...
+ (v_i*D^4*R^3*kp_i^2 - 4*v_i*D^3*R^3*kp_i^2 + 6*v_i*D^2*R^3*kp_i^2 ...
- 2*v_i*D^2*R^2*kp_i^2*r_L - 4*v_i*D*R^3*kp_i^2 + 4*v_i*D*R^2*kp_i^2*r_L ...
+ v_i*L^2*R*ki_i^2 + v_i*R^3*kp_i^2 - 2*v_i*R^2*kp_i^2*r_L ...
+ v_i*R*kp_i^2*r_L^2)*w_v^2 + v_i*D^4*R^3*ki_i^2 - 4*v_i*D^3*R^3*ki_i^2 ...
+ 6*v_i*D^2*R^3*ki_i^2 - 2*v_i*D^2*R^2*ki_i^2*r_L - 4*v_i*D*R^3*ki_i^2 ...
+ 4*v_i*D*R^2*ki_i^2*r_L + v_i*R^3*ki_i^2 - 2*v_i*R^2*ki_i^2*r_L ...
+ v_i*R*ki_i^2*r_L^2))*sin(phi_v)
Answers (1)
syms C D ki_i kp_i L phi_v R r_L v_i w_v
kp_v_out_c = ((w_v^4*(C*D^4*L*R^3*kp_i - 4*C*D^3*L*R^3*kp_i - C*ki_i*D^2*L^2*R^2 ...
+ D^2*L^2*R*kp_i + 6*C*D^2*L*R^3*kp_i + C*r_L*D^2*L*R^2*kp_i + 2*C*ki_i*D*L^2*R^2 ...
- 2*D*L^2*R*kp_i - 4*C*D*L*R^3*kp_i - C*v_i*D*L*R^2*kp_i^2 - 2*C*r_L*D*L*R^2*kp_i ...
- C*ki_i*L^2*R^2 + L^2*R*kp_i - C*ki_i*r_L*L^2*R + r_L*L^2*kp_i + C*L*R^3*kp_i ...
+ C*v_i*L*R^2*kp_i^2 + C*r_L*L*R^2*kp_i) + w_v^2*(6*D^5*R^3*kp_i - D^6*R^3*kp_i ...
+ C*D^4*R^3*ki_i*r_L - 15*D^4*R^3*kp_i + 2*L*D^4*R^2*ki_i - D^4*R^2*kp_i*r_L ...
- 4*C*D^3*R^3*ki_i*r_L + 20*D^3*R^3*kp_i - 8*L*D^3*R^2*ki_i + 2*v_i*D^3*R^2*kp_i^2 ...
+ 4*D^3*R^2*kp_i*r_L + 6*C*D^2*R^3*ki_i*r_L - 15*D^2*R^3*kp_i + 12*L*D^2*R^2*ki_i ...
- 6*v_i*D^2*R^2*kp_i^2 - 6*D^2*R^2*kp_i*r_L + 2*L*D^2*R*ki_i*r_L + D^2*R*kp_i*r_L^2 ...
- 4*C*D*R^3*ki_i*r_L + 6*D*R^3*kp_i - C*L*v_i*D*R^2*ki_i^2 - 8*L*D*R^2*ki_i ...
+ 6*v_i*D*R^2*kp_i^2 + 4*D*R^2*kp_i*r_L - 4*L*D*R*ki_i*r_L - 2*v_i*D*R*kp_i^2*r_L ...
- 2*D*R*kp_i*r_L^2 + C*R^3*ki_i*r_L - R^3*kp_i + C*L*v_i*R^2*ki_i^2 + 2*L*R^2*ki_i ...
- 2*v_i*R^2*kp_i^2 - R^2*kp_i*r_L - C*R*ki_i*r_L^3 + 2*L*R*ki_i*r_L ...
+ 2*v_i*R*kp_i^2*r_L + R*kp_i*r_L^2 + kp_i*r_L^3) - 2*R^2*ki_i^2*v_i ...
+ 2*R*ki_i^2*r_L*v_i + 6*D*R^2*ki_i^2*v_i - 6*D^2*R^2*ki_i^2*v_i ...
+ 2*D^3*R^2*ki_i^2*v_i - 2*D*R*ki_i^2*r_L*v_i)/((L^2*R*kp_i^2*v_i)*w_v^4 ...
+ (v_i*D^4*R^3*kp_i^2 - 4*v_i*D^3*R^3*kp_i^2 + 6*v_i*D^2*R^3*kp_i^2 ...
- 2*v_i*D^2*R^2*kp_i^2*r_L - 4*v_i*D*R^3*kp_i^2 + 4*v_i*D*R^2*kp_i^2*r_L ...
+ v_i*L^2*R*ki_i^2 + v_i*R^3*kp_i^2 - 2*v_i*R^2*kp_i^2*r_L ...
+ v_i*R*kp_i^2*r_L^2)*w_v^2 + v_i*D^4*R^3*ki_i^2 - 4*v_i*D^3*R^3*ki_i^2 ...
+ 6*v_i*D^2*R^3*ki_i^2 - 2*v_i*D^2*R^2*ki_i^2*r_L - 4*v_i*D*R^3*ki_i^2 ...
+ 4*v_i*D*R^2*ki_i^2*r_L + v_i*R^3*ki_i^2 - 2*v_i*R^2*ki_i^2*r_L ...
+ v_i*R*ki_i^2*r_L^2))*cos(phi_v) + (-((C*L^2*R^2*kp_i - 2*C*L^2*R^2*kp_i*D ...
+ C*L^2*R*kp_i*r_L + C*L^2*R^2*kp_i*D^2)*w_v^5 + (L^2*R*ki_i - 2*L*R^2*kp_i ...
+ L^2*ki_i*r_L + C*L*R^3*ki_i + C*R*kp_i*r_L^3 - C*R^3*kp_i*r_L ...
- 2*L*R*kp_i^2*v_i - 2*L^2*R*ki_i*D + 8*L*R^2*kp_i*D - C*R^3*kp_i^2*v_i ...
- 2*L*R*kp_i*r_L + L^2*R*ki_i*D^2 - 12*L*R^2*kp_i*D^2 + 8*L*R^2*kp_i*D^3 ...
- 2*L*R^2*kp_i*D^4 + C*R^2*kp_i^2*r_L*v_i + 6*C*L*R^3*ki_i*D^2 ...
- 4*C*L*R^3*ki_i*D^3 + C*L*R^3*ki_i*D^4 - 6*C*R^3*kp_i*r_L*D^2 ...
+ 4*C*R^3*kp_i*r_L*D^3 - C*R^3*kp_i*r_L*D^4 + 3*C*R^3*kp_i^2*v_i*D ...
+ C*L*R^2*ki_i*r_L + 4*L*R*kp_i*r_L*D - 3*C*R^3*kp_i^2*v_i*D^2 ...
+ C*R^3*kp_i^2*v_i*D^3 - 4*C*L*R^3*ki_i*D + 4*C*R^3*kp_i*r_L*D ...
- 2*L*R*kp_i*r_L*D^2 + 2*L*R*kp_i^2*v_i*D - 2*C*L*R^2*ki_i*r_L*D ...
+ C*L*R^2*ki_i*r_L*D^2 - C*R^2*kp_i^2*r_L*v_i*D)*w_v^3 + (ki_i*r_L^3 ...
- R^3*ki_i + 6*R^3*ki_i*D - 15*R^3*ki_i*D^2 + 20*R^3*ki_i*D^3 - 15*R^3*ki_i*D^4 ...
+ 6*R^3*ki_i*D^5 - R^3*ki_i*D^6 + R*ki_i*r_L^2 - R^2*ki_i*r_L + R*ki_i*r_L^2*D^2 ...
- 6*R^2*ki_i*r_L*D^2 + 4*R^2*ki_i*r_L*D^3 - R^2*ki_i*r_L*D^4 - 2*L*R*ki_i^2*v_i ...
- C*R^3*ki_i^2*v_i - 2*R*ki_i*r_L^2*D + 4*R^2*ki_i*r_L*D + C*R^2*ki_i^2*r_L*v_i ...
+ 3*C*R^3*ki_i^2*v_i*D - 3*C*R^3*ki_i^2*v_i*D^2 + C*R^3*ki_i^2*v_i*D^3 ...
+ 2*L*R*ki_i^2*v_i*D - C*R^2*ki_i^2*r_L*v_i*D)*w_v)/((L^2*R*kp_i^2*v_i)*w_v^4 ...
+ (v_i*D^4*R^3*kp_i^2 - 4*v_i*D^3*R^3*kp_i^2 + 6*v_i*D^2*R^3*kp_i^2 ...
- 2*v_i*D^2*R^2*kp_i^2*r_L - 4*v_i*D*R^3*kp_i^2 + 4*v_i*D*R^2*kp_i^2*r_L ...
+ v_i*L^2*R*ki_i^2 + v_i*R^3*kp_i^2 - 2*v_i*R^2*kp_i^2*r_L ...
+ v_i*R*kp_i^2*r_L^2)*w_v^2 + v_i*D^4*R^3*ki_i^2 - 4*v_i*D^3*R^3*ki_i^2 ...
+ 6*v_i*D^2*R^3*ki_i^2 - 2*v_i*D^2*R^2*ki_i^2*r_L - 4*v_i*D*R^3*ki_i^2 ...
+ 4*v_i*D*R^2*ki_i^2*r_L + v_i*R^3*ki_i^2 - 2*v_i*R^2*ki_i^2*r_L ...
+ v_i*R*ki_i^2*r_L^2))*sin(phi_v)
syms T
RHS = ki_i^2 + kp_i^2*w_v^2;
T2 = isolate(T == RHS, ki_i);
T3 = collect(subs(kp_v_out_c, ki_i, rhs(T2)), T)
%the above is the collected expression, with T substituted for ki_i^2 + kp_i^2*w_v^2
%however, if you substitute the symbols back again then you get a bit of a
%mess. The mess can be simplified somewhat if you assume ki_i is real and
%greater than or equal to 0
subs(T3, T, RHS)
1 Comment
Guilherme
on 21 Jan 2026
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on 21 Jan 2026
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