How to use jacobian after odeToVectorField

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Gabriele COLLA
Gabriele COLLA 2022-11-28
回答： Sakshay 2022-12-1
Ran in:
good evening, i don't understand what's the variables name of the output vector of the function odeToVectorField, the problem is that both the documentation and the vector have this notation Y[1] which is not a possible name for a variable as far as i know. If i try to use Y_1 as a variable it dosen't work but i can't use the real name either because it gives me an error, does anyone have an idea?
syms theta_1(t) theta_2(t) L_1 L_2 m_1 m_2 g
x_1 = L_1*sin(theta_1);
y_1 = -L_1*cos(theta_1);
x_2 = x_1 + L_2*sin(theta_2);
y_2 = y_1 - L_2*cos(theta_2);
vx_1 = diff(x_1);
vy_1 = diff(y_1);
vx_2 = diff(x_2);
vy_2 = diff(y_2);
ax_1 = diff(vx_1);
ay_1 = diff(vy_1);
ax_2 = diff(vx_2);
ay_2 = diff(vy_2);
syms T_1 T_2
eqx_1 = m_1*ax_1(t) == -T_1*sin(theta_1(t)) + T_2*sin(theta_2(t));
eqy_1 = m_1*ay_1(t) == T_1*cos(theta_1(t)) - T_2*cos(theta_2(t)) - m_1*g;
eqx_2 = m_2*ax_2(t) == -T_2*sin(theta_2(t));
eqy_2 = m_2*ay_2(t) == T_2*cos(theta_2(t)) - m_2*g;
Tension = solve([eqx_1 eqy_1],[T_1 T_2]);
eqRed_1 = subs(eqx_2,[T_1 T_2],[Tension.T_1 Tension.T_2]);
eqRed_2 = subs(eqy_2,[T_1 T_2],[Tension.T_1 Tension.T_2]);
L_1 = 1;
L_2 = 1.5;
m_1 = 2;
m_2 = 1;
g = 9.8;
eqn_1 = subs(eqRed_1);
eqn_2 = subs(eqRed_2);
[V,S] = odeToVectorField(eqn_1,eqn_2);
jacob = jacobian(V,sym('Y',[1 4]))
jacob = 
subs(jacob,sym('Y',[1 4]),[0 0 0 0])
ans = 
sym('Y[1]')
Error using sym>convertChar
Character vectors and strings in the first argument can only specify a variable or number. To evaluate character vectors and strings representing symbolic expressions, use 'str2sym'.

Error in sym>tomupad (line 1624)
S = convertChar(x);

Error in sym (line 397)
S.s = tomupad(x);
  1 个评论
Paul
Paul 2022-11-28
编辑：Paul 2022-11-28
Hi Gabriele,
It's a mystery to me as well: link to question.
It seems like the only real use of the outputs are as inputs to matlabFunction for numerical solution of the ODE via the suited of ode solvers.

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回答（1 个）

Sakshay
Sakshay 2022-12-1
Hello Gabriele,
As per my understanding you want to use the output of the "odeToVectorField" for further processing using symbolic expressions, like the "jacobian" function.
Currently, MATLAB only supports generating a "matlabFunction" from the output of "odeToVectorField" function. The symbolic variable used to construct the output of “odeToVectorField” is “Y”. This variable allows for the generation of a MATLAB function handle.
However, you can use a workaround for the same to convert the “Y[i]” to “yi”, in the output of “odeToVectorField” function. This would enable to use this output in the “jacobian” function for further processing. A sample code would look like:
% Convert the Y[i] in odeToVectorField output V to yi
V_c = feval(symengine,'evalAt',V,'Y=[y1,y2,y3,y4]');
% Evaluate jacobian with respect to yi
jacob = jacobian(V_c, sym('y', [1 4]));
For more information on "odeToVectorField" function, you can refer to the following documentation:
Reduce order of differential equations to first-order - MATLAB odeToVectorField (mathworks.com)

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