functionalDerivative, deriving as function of derivative?

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Dan D 2016-2-8

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https://ww2.mathworks.cn/matlabcentral/answers/267221-functionalderivative-deriving-as-function-of-derivative

评论： Dan D 2016-2-8

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Hello all,

I'm attempting to compute a Lagrangian EQs of motion.

Part of this requires computing the partial derivative of L with respect to variable_dot, the derivative of the variable.

syms t m1 m2 x1(t) x2(t) k
K = (1/2)*m1*diff(x1,t)^2;
P = (sym(1)/2)*k*(x1-x2)^2;
L = K - P
diff( functionalDerivative( L, diff(x1)) ,t) - functionalDerivative(L,x1)

functionalDerivative() does not like the form of the "diff(x1)". Is there a way to do this?

Thanks a lot, Dan

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Answer 1

John BG 2016-2-8

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/267221-functionalderivative-deriving-as-function-of-derivative#answer_209074

Takeshita san has a detailed explanation how to solve the Euler-Lagrange equation with MuPAD:

http://uk.mathworks.com/matlabcentral/fileexchange/42196-euler-lagrange-equation?s_tid=srchtitle

If you find this link useful, please click on the thumbs-up vote link above,

thanks in advance

John

jgb2012@sky.com

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Dan D 2016-2-8

I was hoping that the new functionalDerivative() function would make this a little cleaner. it works great for the partial derivative in respect to x(t), it just doesn't seem to be able to handle diff(x(t)) as a parameter.

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