Re: Help with solving ODE
- To: mathgroup at smc.vnet.net
- Subject: [mg81860] Re: [mg81772] Help with solving ODE
- From: DrMajorBob <drmajorbob at bigfoot.com>
- Date: Fri, 5 Oct 2007 04:49:11 -0400 (EDT)
- References: <5680378.1191487402725.JavaMail.root@m35>
- Reply-to: drmajorbob at bigfoot.com
Clear[x, y]
DSolve[{I y''[x] + k y'[x] == 2 G M m d/a^2, y[0] == 0, y'[0] ==
= 0},
y, x];
y[x_] = y[x] /. First@%
(2 d G m M (-\[ImaginaryI] + \[ImaginaryI] \[ExponentialE]^(\
\[ImaginaryI] k x) + k x))/(a^2 k^2)
Bobby
On Wed, 03 Oct 2007 01:31:57 -0500, Pioneer1 <1pioneer1 at gmail.com> wrote:
> Hi,
>
> Can anyone help solve this linearized differential equation:
>
> Iy'' + ky' = 2GMmd/a^2
>
> Primes are time derivates of y (=theta=excursion angle). Is it
> possible to solve this for the initial conditions y(0)=0 and y'(0)==
0?
>
> I got the solution at sci.math for the non-linear version and I want
> to compare the two. Here's the link to sci.math thread:
>
> http://groups.google.com/group/sci.math/browse_thread/thread/a6ee2f782df09625/53cf5573d354a3ab#53cf5573d354a3ab
>
> Further information is also available at sci.physics.research
>
> http://groups.google.com/group/sci.physics.research/browse_thread/thread/d391940cc173f9dc/eed90e6c3fee0edc#eed90e6c3fee0edc
>
> Parameters are:
>
>> y = theta = excursion angle in radians
>> A = I = moment of inertia = 13,138,117.34 g cm^2
>> B = R = damping = for now I assume this to be zero
>> C = k = torsion constant = 724.68 g cm^2 sec^-2
>> d = moment arm = 93.09 cm
>> D = 2GMmd = 2 * 6.67*10^-8 * 158100 * 729.8 * 93.09 = 1432.82
>> a = distance between weights = 22.10 cm
>
> I would truly appreciate help with this. Thanks
>
>
>
--
DrMajorBob at bigfoot.com