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How to symbolically derive a function with respect to a function

sfan
1-Newbie

How to symbolically derive a function with respect to a function

Please see the attachment.

In Lagrange Equation for Dynamic equation,

there is a term that request the derivative of T(t) with respect to (u(t))',

I don't know how to achieve this.

Looking forward to your help!

Thank you very much!

1 ACCEPTED SOLUTION

Accepted Solutions
LucMeekes
23-Emerald III
(To:sfan)

From what I see you have this (assuming your formulation is correct):

Which means you have a function T(t) which is found from the function u2(t) by first taking the derivative of u2(t) with respect to time: u'(t)=d/dt of u(t). Then square the resulting function squ'(t)=u'(t)*u'(t). Then multiply the result with a constant (assuming that a, b, and the three m's are known). This should be simple, provided that u2(t) is given...

Are you sure you don't need a second derivative of any functions u and v, rather that the first derivative squared...?

Success!
Luc

View solution in original post

3 REPLIES 3
LucMeekes
23-Emerald III
(To:sfan)

From what I see you have this (assuming your formulation is correct):

Which means you have a function T(t) which is found from the function u2(t) by first taking the derivative of u2(t) with respect to time: u'(t)=d/dt of u(t). Then square the resulting function squ'(t)=u'(t)*u'(t). Then multiply the result with a constant (assuming that a, b, and the three m's are known). This should be simple, provided that u2(t) is given...

Are you sure you don't need a second derivative of any functions u and v, rather that the first derivative squared...?

Success!
Luc

sfan
1-Newbie
(To:LucMeekes)

Hi, Luc

So by this step,

Capture.JPG

Is it possible to let Mathcad derive T(t) with respect to du2(t)/dt?

Which will result in:

Capture.JPG

It is to set du2(t)/dt as the argument and the others (including u2(t), if exists) as constants.

Thank you

Best

Shawn

LucMeekes
23-Emerald III
(To:sfan)

Hi Shawn,

No, If you feed that first expression AND u2(t) to Mathcad it will take the deriverative of u2(t), then square it and multiply the resulting function with the constant involving a, b and the three m's. The result you mention is NOT obtained.

Observe my question/comment at the end of my first reply:

Success!
Luc

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