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Thread Subject:
coupled ode

Subject: coupled ode

From: deepak

Date: 27 Jun, 2010 13:44:04

Message: 1 of 3

I have two odes as

K(l-(x2-x1-l)/cos(a2))*cos(a2) -c(x2'-x1')=((x1’’*cos(2*a2 - a1))/2 + 2*g*sin(a1) + 12*x1’’*cos(a1) + 2*g*sin(a1 - 2*a2) - (5*x1’’*cos(a1 - 2*a2))/2 - 2*x1’’*cos(a1 + 2*a2))/(4*(cos(2*a1) + cos(2*a2) - cos(2*a1 - 2*a2)/2 - cos(2*a1 + 2*a2)/2 + 3)) + cot(a2)/(cos(a1)*(1/sin(a2)^2 + cot(a2)^2/cos(a1)^2 + cot(a2)^2*tan(a1)^2 + 1)^(1/2))

and,

K(l-(x1-x3)/cos(a2))*cos(a2) -c(x1'-x3')=1/(sin(a2)*(1/sin(a2)^2 + cos(a2)^2/(cos(a1)^2*sin(a2)^2) + (cos(a2)^2*sin(a1)^2)/(cos(a1)^2*sin(a2)^2) + 1)^(1/2)) - (2*g*sin(a2) - 12*x1’’*(2*sin(a2/2)^2 - 1) - 2*g*sin(2*a1 - a2) + 2*x1’’*(2*sin(a1 - a2/2)^2 - 1) + 2*x1’’*(2*sin(a1 + a2/2)^2 - 1))/(4*(sin(a1 + a2)^2 - 2*sin(a1)^2 - 2*sin(a2)^2 + sin(a1 - a2)^2 + 4))

where
g=9.8m/s^2
x3'= constant and known
and a1 and a2 are known as well.
so there are 6 unknown x1,x2,x3 and x1',x2' and x3'' and two second order odes.

Now you can see that converting it into system of nice looking single order odes is tough. is there any way i can solve it without doing that or how can i convert it into system of single order odes

Thanks

Subject: coupled ode

From: deepak

Date: 27 Jun, 2010 13:52:05

Message: 2 of 3

sorry the unknowns are x1,x2,x3,x1',x2',x1''.

thanks

Subject: coupled ode

From: Faraz Afzal

Date: 27 Jun, 2010 16:25:23

Message: 3 of 3

"deepak " <dkjknobel@rediff.com> wrote in message <i07kj4$phq$1@fred.mathworks.com>...
> I have two odes as
>
> K(l-(x2-x1-l)/cos(a2))*cos(a2) -c(x2'-x1')=((x1’’*cos(2*a2 - a1))/2 + 2*g*sin(a1) + 12*x1’’*cos(a1) + 2*g*sin(a1 - 2*a2) - (5*x1’’*cos(a1 - 2*a2))/2 - 2*x1’’*cos(a1 + 2*a2))/(4*(cos(2*a1) + cos(2*a2) - cos(2*a1 - 2*a2)/2 - cos(2*a1 + 2*a2)/2 + 3)) + cot(a2)/(cos(a1)*(1/sin(a2)^2 + cot(a2)^2/cos(a1)^2 + cot(a2)^2*tan(a1)^2 + 1)^(1/2))
>
> and,
>
> K(l-(x1-x3)/cos(a2))*cos(a2) -c(x1'-x3')=1/(sin(a2)*(1/sin(a2)^2 + cos(a2)^2/(cos(a1)^2*sin(a2)^2) + (cos(a2)^2*sin(a1)^2)/(cos(a1)^2*sin(a2)^2) + 1)^(1/2)) - (2*g*sin(a2) - 12*x1’’*(2*sin(a2/2)^2 - 1) - 2*g*sin(2*a1 - a2) + 2*x1’’*(2*sin(a1 - a2/2)^2 - 1) + 2*x1’’*(2*sin(a1 + a2/2)^2 - 1))/(4*(sin(a1 + a2)^2 - 2*sin(a1)^2 - 2*sin(a2)^2 + sin(a1 - a2)^2 + 4))
>
> where
> g=9.8m/s^2
> x3'= constant and known
> and a1 and a2 are known as well.
> so there are 6 unknown x1,x2,x3 and x1',x2' and x3'' and two second order odes.
>
> Now you can see that converting it into system of nice looking single order odes is tough. is there any way i can solve it without doing that or how can i convert it into system of single order odes
>
> Thanks

Oh Gosh
U have no idea it seems flooding NEWSREADER..

Send me your equation in written or latex file and tell me which variables are of your interest. I hope i will be able to put it into nice looking ode.

Regards,
Faraz

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