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Thread Subject:
Solve problem

Subject: Solve problem

From: Vlastimil Cervenka

Date: 9 Jan, 2009 21:24:01

Message: 1 of 3

Hi,

I have cycloid X=[t-c*sin(t),1-c*cos(t)] and I want to find c parameters so that the cycloid has a singular points. I differentiate into dX variable and put the solve(dX). Problem is, that Matlab returns only the one result (c=1,t=0) but there is still another one (c=-1,t=pi) which Matlab does not return to me. Do you know why is it so. Thank you for your response.

Subject: Solve problem

From: Roger Stafford

Date: 10 Jan, 2009 02:10:03

Message: 2 of 3

"Vlastimil Cervenka" <armstrong2free@seznam.cz> wrote in message <gk8f9h$2jn$1@fred.mathworks.com>...
> Hi,
>
> I have cycloid X=[t-c*sin(t),1-c*cos(t)] and I want to find c parameters so that the cycloid has a singular points. I differentiate into dX variable and put the solve(dX). Problem is, that Matlab returns only the one result (c=1,t=0) but there is still another one (c=-1,t=pi) which Matlab does not return to me. Do you know why is it so. Thank you for your response.

  By "singular" you apparently mean points where both components of X have zero derivatives with respect to t. There are infinitely many solutions to that condition, as you can easily show since the sine and cosine functions are periodic with a period of 2*pi. What is it you would expect 'solve' to return in the finite amount of time it has available? In any case, Mathworks' documentation does not promise to return all possible roots. Sometimes it is unable to return even one.

Roger Stafford

Subject: Solve problem

From: Srikanth

Date: 10 Jan, 2009 05:06:25

Message: 3 of 3

On Jan 9, 2:24=A0pm, "Vlastimil Cervenka" <armstrong2f...@seznam.cz>
wrote:
> Hi,
>
> I have cycloid X=3D[t-c*sin(t),1-c*cos(t)] and I want to find c parameter=
s so that the cycloid has a singular points. I differentiate into dX variab=
le and put the solve(dX). Problem is, that Matlab returns only the one resu=
lt (c=3D1,t=3D0) but there is still another one (c=3D-1,t=3Dpi) which Matla=
b does not return to me. Do you know why is it so. Thank you for your respo=
nse.

You could try specifying initial conditions if you know a
neighbourhood for the solution - it will still return just one root,
but you can (to some extent) decide which root it will be.

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