hi there i want to get the values of A1,A2,A2,Q1,Q2,Q3 , i have six equations and six initial conditions as Xo, Vo kindly suggest me solution

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Rahul Jangid 2022-8-2

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1772405-hi-there-i-want-to-get-the-values-of-a1-a2-a2-q1-q2-q3-i-have-six-equations-and-six-initial-condit

评论： Rahul Jangid 2022-8-3

for i = 1:1:3 
    x(t) = U(i,1)*A1*cos(w2(1,1)*t + Q1) + U(i,2)*A2*cos(w2(2,2)*t + Q2) +U(i,3)*A3*cos(w2(3,3)*t + Q3);
    x= x(t);
    v= diff(x(t));
   
end
x
v
Xo = [1 0 0]
Vo = [0 0 0]
% eqns = [x(1,1) == Xo(1,1) , x(1,2) == Xo(1,2), x(1,3) == Xo(1,3), v(1,1) == Vo(1,1) , v(1,2) == Vo(1,2), v(1,3) == Vo(1,3)];
% S = solve(eqns,[A1 A2 A3 Q1 Q2 Q3])

采纳的回答

Walter Roberson 2022-8-2

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1772405-hi-there-i-want-to-get-the-values-of-a1-a2-a2-q1-q2-q3-i-have-six-equations-and-six-initial-condit#answer_1019595

在 MATLAB Online 中打开

for i = 1:1:3 
  x{i} = U(i,1)*A1*cos(w2(1,1)*t + Q1) + U(i,2)*A2*cos(w2(2,2)*t + Q2) +U(i,3)*A3*cos(w2(3,3)*t + Q3);
  v{i} = diff(x{i}, t);
end
Xo = [1 0 0]
Vo = [0 0 0]
eqns = [x{1} == Xo(1,1) , x{2} == Xo(1,2), x{3} == Xo(1,3), v{1} == Vo(1,1) , v{2} == Vo(1,2), v{3} == Vo(1,3)];
S = solve(eqns,[A1 A2 A3 Q1 Q2 Q3])

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Walter Roberson 2022-8-2

编辑：Walter Roberson 2022-8-2

在 MATLAB Online 中打开

%% Intoroduction of variables

syms m k F1 F2 F3 A1 A2 A3 Q1 Q2 Q3 t

%% Value submission

m=1;

k=1;

% w=1;

%% Mass, Stiffness AND Force matrices

M=[m 0 0

0 m 0

0 0 m];

K = [2*k -k 0

-k 2*k -k

0 -k k] ;

%% Equation of motion

format short

[U,w2] = eig(K,M)

U = 3×3

-0.3280 0.7370 -0.5910 -0.5910 0.3280 0.7370 -0.7370 -0.5910 -0.3280

w2 = 3×3

0.1981 0 0 0 1.5550 0 0 0 3.2470

%% Response of the system (here A and Q shows the amplitude and phase difference)

format short

for i = 1:1:3

x{i} = U(i,1)*A1*cos(w2(1,1)*t+Q1) + U(i,2)*A2*cos(w2(2,2)*t+Q2) +U(i,3)*A3*cos(w2(3,3)*t+Q3);

v{i} = diff(x{i}, t);

end

x = 1×3 cell array

{[(6638091741507547*A2*cos(Q2 + (7002908864245409*t)/4503599627370496))/9007199254740992 - (2661668130624679*A3*cos(Q3 + (913943508336349*t)/281474976710656))/4503599627370496 - (5908457496031831*A1*cos(Q1 + (3567972556901945*t)/18014398509481984))/18014398509481984]} {[(2954228748015915*A2*cos(Q2 + (7002908864245409*t)/4503599627370496))/9007199254740992 + (1659522935376887*A3*cos(Q3 + (913943508336349*t)/281474976710656))/2251799813685248 - (332708516328085*A1*cos(Q1 + (3567972556901945*t)/18014398509481984))/562949953421312]} {[- (5323336261249361*A2*cos(Q2 + (7002908864245409*t)/4503599627370496))/9007199254740992 - (2954228748015915*A3*cos(Q3 + (913943508336349*t)/281474976710656))/9007199254740992 - (6638091741507549*A1*cos(Q1 + (3567972556901945*t)/18014398509481984))/9007199254740992]}

v = 1×3 cell array

{[(2432614309330170770701412156971*A3*sin(Q3 + (913943508336349*t)/281474976710656))/1267650600228229401496703205376 - (46485951498277445065388233601723*A2*sin(Q2 + (7002908864245409*t)/4503599627370496))/40564819207303340847894502572032 + (21081214199463155606688465811295*A1*sin(Q1 + (3567972556901945*t)/18014398509481984))/324518553658426726783156020576256]} {[(1187094855706169954794794625325*A1*sin(Q1 + (3567972556901945*t)/18014398509481984))/10141204801825835211973625643008 - (1516710213722988286690676565563*A3*sin(Q3 + (913943508336349*t)/281474976710656))/633825300114114700748351602688 - (20688194686489267889392397684235*A2*sin(Q2 + (7002908864245409*t)/4503599627370496))/40564819207303340847894502572032]} {[(37278838691262164489772848433649*A2*sin(Q2 + (7002908864245409*t)/4503599627370496))/40564819207303340847894502572032 + (2699998186389765280096224994335*A3*sin(Q3 + (913943508336349*t)/281474976710656))/2535301200456458802993406410752 + (23684529163896374554619270282805*A1*sin(Q1 + (3567972556901945*t)/18014398509481984))/162259276829213363391578010288128]}

Xo = [1 0 0];

Vo = [0 0 0];

% eqns = [x(1,1) == Xo(1,1) , x(1,2) == Xo(1,2), x(1,3) == Xo(1,3), v(1,1) == Vo(1,1) , v(1,2) == Vo(1,2), v(1,3) == Vo(1,3)];

eqns = [x{1} == Xo(1,1) , x{2} == Xo(1,2), x{3} == Xo(1,3), v{1} == Vo(1,1) , v{2} == Vo(1,2), v{3} == Vo(1,3)];

sol = solve(eqns, [A1 A2 A3 Q1 Q2 Q3])

sol = struct with fields:

A1: [8×1 sym] A2: [8×1 sym] A3: [8×1 sym] Q1: [8×1 sym] Q2: [8×1 sym] Q3: [8×1 sym]

cross_check = subs(lhs(eqns) - rhs(eqns), sol)

cross_check =