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From: Andreas Karpf on 11 Apr 2010 17:19
dear community!

i have got a question with the following paper on page 10:

http://www.dur.ac.uk/t.i.renstrom/research/dynamic.pdf

Especially I don't have a clue how to solve from first order equations 7 - 9 to
equations 11 - 14 as suggested in the paper. If anybody could give me a hint
or explanation how to do this, this would be so great!!!!!

Thank you very much!

Andi

From: Alois Steindl on 12 Apr 2010 04:25
Hello,
you should remember the math lecture(s) about implicit functions:
(7) and (8) are two equations for the variables c and l. The author
assumes, that these equations can be solved, so you get
c and l as functions of q and omega. Suppressing the argument t for
simplicity, you can rewrite (8) in the following way:
u_c(c(q, omega), l(q, omega)) - q = 0. (8a)
(You also get an analogous equation (9a) for (9)).

Partially differentiating (8a) and (9a) w.r.t q gives
u_cc c_q + u_cl l_q - 1 = 0
u_lc c_q + u_ll l_q + omega = 0
which is a linear equation for c_q and l_q.

It's really basic calculus.

Good luck
Alois


--
Alois Steindl, Tel.: +43 (1) 58801 / 32558
Inst. for Mechanics and Mechatronics Fax.: +43 (1) 58801 / 32598
Vienna University of Technology, A-1040 Wiedner Hauptstr. 8-10
From: Arno Narque on 12 Apr 2010 07:55
On 2010-04-12 10:25:04 +0200, Alois Steindl said:

> Hello,
> you should remember the math lecture(s) about implicit functions:
> (7) and (8) are two equations for the variables c and l. The author
> assumes, that these equations can be solved, so you get
> c and l as functions of q and omega. Suppressing the argument t for
> simplicity, you can rewrite (8) in the following way:
> u_c(c(q, omega), l(q, omega)) - q = 0. (8a)
> (You also get an analogous equation (9a) for (9)).
>
> Partially differentiating (8a) and (9a) w.r.t q gives
> u_cc c_q + u_cl l_q - 1 = 0
> u_lc c_q + u_ll l_q + omega = 0
> which is a linear equation for c_q and l_q.
>
> It's really basic calculus.
>
> Good luck
> Alois
>
>

Oh man you are great, thank you very very much! That's great! Merci
beaucoup, vielen vielen Dank!

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