How do you take the partial derivative of a function relative to theta dot

Question

Cason Cox 2022-11-29

1
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1866838-how-do-you-take-the-partial-derivative-of-a-function-relative-to-theta-dot

编辑： Andreas Apostolatos 2022-11-29

采纳的回答： Andreas Apostolatos

Need to take the partial derivative of l with respect to theta 1 dot

clear; clc;

syms theta1(t) theta2(t) r1 r2 m1 m2 g

%theta1dot=diff(theta1)

%theta2dot=diff(theta2)

x1 = r1*sin(theta1);

y1 = -r1*cos(theta1);

x2 = x1+r2*sin(theta2+theta1);

y2 = y1-r2*cos(theta2+theta1);

x1dot=diff(x1)

y1dot=diff(y1);

x2dot=diff(x2);

y2dot=diff(y2);

pe=m1*g*y1+m2*g*y2;

ke=1/2*m1*(x1dot^2+y1dot^2)+1/2*m2*(x2dot^2+y2dot^2);

l=ke-pe

diff(l,theta1)

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Answer 1

Andreas Apostolatos 2022-11-29

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1866838-how-do-you-take-the-partial-derivative-of-a-function-relative-to-theta-dot#answer_1115608

编辑：Andreas Apostolatos 2022-11-29

在 MATLAB Online 中打开

Hi Cason,

You can achieve this workflow by substituting the symbolic expression diff(theta1) with a symbolic variable theta1dot in expression l(t), take the derivative of that expression with respect to theta1dot and finally substitute back symbolic variable theta1dot with diff(theta1) in the resulting expression, namely,

syms theta1dot
subs(diff(subs(l(t), diff(theta1(t)), theta1dot), theta1dot), theta1dot, diff(theta1(t)))

I have cascaded all underlying operations, but feel free to expand them in multiple lines of code to get a more readable version of the latter one. For more information on function subs, please read the corresponding documentation page,

https://www.mathworks.com/help/symbolic/subs.html

I hope this helps.

Kind regards

Andreas