# Subs dosen't work with one argument

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Sergey Bondarenko
on 8 Mar 2021

Commented: Walter Roberson
on 16 Mar 2021

I want to use subs to subsistute some constants in my equations, but I get error when I try to do it.

There is code of my calculation:

clc;

clear;

clearvars;

syms X(t) Y(t) alpha(t) beta(t) theta(t);

syms phi(t) [2 2];

syms chi m_0 g M_z s_0 gamma_0 J_t_0 J_p_0 real;

syms c l [1 3] real;

syms h r J_t J_p s gamma m M [1 2] real;

syms R_Et R_E [3 2];

syms R_Bt R_B [3 4];

syms J_E [3 3 2]

syms d [1 5] real;

syms R_G [3 1];

J_G = diag([J_t_0, J_t_0, J_p_0]);

J_E(:,:,1) = diag([J_t1, J_t1, J_p1]);

J_E(:,:,2) = diag([J_t2, J_t2, J_p2]);

R_C = [X;Y;0];

R_Gt = [s_0*cos(gamma_0);s_0*sin(gamma_0);0];

R_Bt(:,1) = [r1*cos(phi1_1);r1*sin(phi1_1);0];

R_Bt(:,2) = [r1*cos(phi2_1);r1*sin(phi2_1);0];

R_Bt(:,3) = [r2*cos(phi1_2);r2*sin(phi1_2);0];

R_Bt(:,4) = [r2*cos(phi2_2);r2*sin(phi2_2);0];

R_Et(:,1) = [s1*cos(gamma1);s1*sin(gamma1);h1];

R_Et(:,2) = [s2*cos(gamma2);s2*sin(gamma2);h2];

P_alpha = [[1 0 0];

[0 cos(alpha) sin(alpha)];

[0 -sin(alpha) cos(alpha)]];

P_beta = [[cos(beta) 0 -sin(beta)];

[0 1 0];

[sin(beta) 0 cos(beta)]];

P_theta = [[cos(theta) sin(theta) 0];

[-sin(theta) cos(theta) 0];

[0 0 1]];

A = P_theta*P_beta*P_alpha;

for_assume = [alpha, beta];

for_assume = transpose(symToVector(for_assume, 2));

A = assumeSmallTrig(A, for_assume);

A = assumeSmall(A,for_assume, 0);

P_chi = [[cos(chi) 0 -sin(chi)];%why???????

[0 1 0];

[sin(chi) 0 cos(chi)]];

Omega = P_chi*(P_theta*P_beta*[diff(alpha);0;0] + ...

P_theta*[0;diff(beta);0] + [0;0;diff(theta)]);

for_assume = [alpha, beta, chi];

for_assume = transpose(symToVector(for_assume, 3));

Omega = assumeSmallTrig(Omega, for_assume);

R_G = R_C + transpose(A)*R_Gt;

R_G = simplify(R_G, "Steps",30);

for j = 1:2

R_E(:,j) = R_C + transpose(A)*R_Et(:,j);

R_E(:,j) = simplify(R_E(:,j), "Steps",30);

end

for j = 1:2

R_B(:,j) = R_E(:,1) + transpose(A)*R_Bt(:,j);

R_B(:,j+2) = R_E(:,2) + transpose(A)*R_Bt(:,j+2);

R_B(:,j) = simplify(R_B(:,j), "Steps",30);

R_B(:,j+2) = simplify(R_B(:,j+2), "Steps",30);

end

v_r = symToVector(diff(R_G, 't'),3);

syms T V D;

T = 0; V =0; D = 0;

temp = [phi1_1(t), phi2_1(t), phi1_2(t), phi2_2(t)];

for j = 1:2

v_o = diff(R_E(:,j), 't');

v_b_1 = diff(R_B(:,j), 't');

v_b_2 = diff(R_B(:,j+2), 't');

T = T + M(j)*(v_o(1)^2+v_o(2)^2) + transpose(Omega)*(J_E(:,:,j)*Omega) + ...

m(1)*(v_b_1(1)^2+v_b_1(2)^2) + m(2)*(v_b_2(1)^2+v_b_2(2)^2);

V = V + M(j)*g*R_E(1,j) + m(1)*g*R_B(1,j) + m(2)*g*R_B(1,j+2);

D = D + d4/2*diff(temp(j))^2 + d5/2*diff(temp(j+2))^2;

end

T = T/2 + 1/2*(m_0*(v_r(1)^2+v_r(2)^2)+transpose(Omega)*(J_G*Omega));

R_G = symToVector(R_G,3);

V = V + c1/2*((X-l1*beta)^2+(Y+l1*alpha)^2)+...

c2/2*((X+l2*beta)^2+(Y-l2*alpha)^2) + m_0*g*R_G(1);

D = D + d1/2*((diff(X)-l1*diff(beta))^2+(diff(Y)+l1*diff(alpha))^2)+...

d2/2*((diff(X)+l2*diff(beta))^2+(diff(Y)-l2*diff(alpha))^2)+...

d3/2*(diff(theta)^2);

L = T - V;

Lagr = sym(zeros(9,1));

Lagr_r = [0; 0; M_z*beta; 0; M_z; 0; 0; 0; 0];

Lagr_r = symToVector(Lagr_r, 9);

temp_1 = [X(t), Y(t), alpha(t), beta(t), theta(t), ...

phi1_1(t), phi2_1(t), phi1_2(t), phi2_2(t)];

for_assume = [alpha, beta, chi];

for_assume = transpose(symToVector(for_assume, 3));

for i = 1:9

Lagr(i) = diff(diff(L,diff(temp_1(i),t)),t) - diff(L,temp_1(i)) + diff(D,diff(temp_1(i),t));

Lagr(i) = assumeSmall(Lagr(i),for_assume,2);

end

Lagr = simplify(Lagr);

Lagr = Lagr - Lagr_r;

s_0 = 0.01; gamma_0 = 0.01; chi = 0.02; s1 = 0.001;

s2 = 0.001; gamma1 = 1; gamma2 = 1+pi/2; m_0 = 10; l0 = 1;

r1 = l0/10; r2 = l0/10;

l1 = 0.5; l2 = l0-l1; J_p_0 = m_0*(r2)^2/8;

J_t_0 = J_p/2 + m_0*l0^2/12; m1=0.375;m2 = 0.375;

d1 = 100; d2 = 100; d3 = 2; d4 = 10; d5= 10;

h1 = 0.45; h2 = -0.45; c1 = 2*10^5; c2 = 2*10^5;

M_z = 2000; omega = 600; g = 9.81;

J_p1 = m1*(r1)^2/8; J_t1 = J_p1/2; M1 = 0.5;

J_p2 = m2*(r2)^2/8; J_t2 = J_p2/2; M2 = 0.5;

lagr_subs = subs(Lagr);

Error ocurs in last string. It is:

Error using mupadengine/feval_internal

Two arguments expected.

Error in sym/subs (line 93)

X{k} = symfun(feval_internal(symengine,X{k},args_c{:}),args);

I don't understand how to fix it. If somebody have sugestions or had that trouble before, please give me advice.

##### 0 Comments

### Accepted Answer

Raynier Suresh
on 16 Mar 2021

Edited: Raynier Suresh
on 16 Mar 2021

Hi,The error is due to the symbolic variable beta(t), beta is an inbuilt function with two arguments. To understand this try the below code

%% No Error Will occur

syms Beta(t)

subs(Beta)

%% Because of conflict with an internal function error will occur

syms beta(t)

subs(beta)

To avoid this use a different name for beta variable. Your code works fine once the beta is renamed.

### More Answers (1)

Raynier Suresh
on 16 Mar 2021

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