Re: Using InterpolateRoot Function in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg41212] Re: Using InterpolateRoot Function in Mathematica
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Wed, 7 May 2003 03:58:07 -0400 (EDT)
- References: <b981k9$642$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Bobby,
Just a question: is the line
z[L_,x_]=-(2*x*(...
a typing error, i.e. shouldn't it read
z[L_,x_]:=-(2*x*(...?
Or is a definition like that possible, and if so, what does it mean?
Regards,
Wolfgang
Bobby Treat wrote:
> Needs["NumericalMath`InterpolateRoot`"]
> z[L_,x_]=-(2*x*(L*beta-3*deltaY))/L^2-(3*x^2*((-L)*beta+2*deltaY))/L^3;
> deltaY=0.000254;L0=.013;alpha=5;
> beta=Tan[alpha*(Pi/180)];
> f[L_?NumericQ]:=NIntegrate[Sqrt[1+z[L,x]^2],{x,0,L}]-L0
> InterpolateRoot[f[L],{L,.01,.02}]
>
> {L -> 0.012992620790646777121996501}
>
> NIntegrate and NumericQ help avoid the messy symbolic integral. Making
> z an explicit function isn't essential, but I gave up getting past
> NIntegrate's HoldAll attribute without it.
>
> Bobby
>
> -----Original Message-----
> From: Haritha Yalamanchili <haritha12 at attbi.com>
To: mathgroup at smc.vnet.net
> mathgroup at smc.vnet.net
> Subject: [mg41212] Re: Using InterpolateRoot Function in Mathematica
>
> Hi Bobby,
>
> Thank you for the response. I did not enter the exact mathematica
> format, I
> only used the symbolic notation to explain the problem (sorry if this
> caused
> any confusion). Attached is the mathematica file I was using to solve
> for
> the arclength.
>
> deltay, beta and L0 are constants. Also L0 can be used as an initial
> guess
> for the root (L).
>
> I was able to solve this problem in Mathcad, on one of my friends
> computer,
> but I would prefer to solve in Mathematica , as I am more comfortable
> using
> Mathamatica.
>
> Any help that you could provide is greatly appreciated.
>
> Thank You
> Prasad
> ----- Original Message -----
> From: "Bobby Treat" <drmajorbob+MathGroup3528 at mailblocks.com>
To: mathgroup at smc.vnet.net
> Subject: [mg41212] Re: Using InterpolateRoot Function in Mathematica
>
>
>
>>First, why write
>>
>>f(L) = Integrate[sqrt(1+z^2) dx] - L0 (Integration limits are from 0
>>
> to
>
>>L)
>>
>>if you mean
>>
>>f[L_]:= Integrate[sqrt(1+z^2),{z,0,L}] - L0
>>
>>??
>>
>>This leaves me wondering if you entered that, or something else. The
>>possible errors you MIGHT have made are endless, so it would really
>>help if you just showed us the statement you entered.
>>
>>Secondly, what is L0? Another unknown? A parameter?
>>
>>Bobby
>>
>>-----Original Message-----
>>From: Haritha Yalamanchili <haritha12 at attbi.com>
To: mathgroup at smc.vnet.net
>>To: mathgroup at smc.vnet.net
>>Sent: Sun, 4 May 2003 03:56:52 -0400 (EDT)
>>Subject: [mg41212] Using InterpolateRoot Function in Mathematica
>>
>>Hi,
>>
>>I am trying to use Mathematica to find a value of "L" that satisfies
>>
> the
>
>>equation
>>
>>Integrate[sqrt(1+z^2) dx] - L0 = 0 (Integration limits are from 0 to
>>
> L)
>
>>where,
>>
>>z= -2 x(L C1 - 3 C2)/L^2 - 3 x^2(-L C1 + 2 C2)/L^3
>>
>>In order to find the value of L that satisfies the above equation, I
>>have
>>setup the problem in Mathematica as shown below. Can some one help to
>>verify
>>if the problem is setup properly of if Mathematica is capable of
>>finding a
>>root for such functions.
>>
>>******
>>f(L) = Integrate[sqrt(1+z^2) dx] - L0 (Integration limits are from 0
>>
> to
>
>>L)
>>
>>InterpolateRoot[ f(L),{L,0,L0} ]
>>*******
>>(L0=13, C1=0.12, C2=0.25)
>>
>>Value of L is close to L0 and hence, L0 can be used as the initial
>>
> guess
>
>>value.
>>
>>Thank You and Best Regards
>>Prasad
>>
>