Re: need help determined time to travel a path

• To: mathgroup at smc.vnet.net
• Subject: [mg107530] Re: [mg107512] need help determined time to travel a path
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Tue, 16 Feb 2010 03:52:05 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <201002151047.FAA28291@smc.vnet.net>

```The mystery to me is why you're getting any result at all.

First, built-in objects in Mathematica always begin with an upper-case
letter.  Thus:  Pi, not pi.

Second, you use "g" in the Integrate, but there is no g defined anywhere

Third, your Integrate uses time0, but no time0 has been defined anywhere

Fourth, Sin[t+Pi] is the same as -Sin[t], and Cos[t+Pi] is the same as
-Cos[t].

Fifth, I presume thatyour time0 is actually the value 0.01 that is the
lower limit on the integral.  Assuming that's so, then you have here
circley[time0] < circley[t] which means you're taking the square root of
a negative quantity.  So I think you want the reverse, namely,
circley[t]- circley[0.01].

Sixth, there's no need whatsoever for the * symbol in your code to
denote multiplication. As in writing math, juxtaposition denotes
multiplication, so that 2g is the product of 2 with g, and
2g(circley[t]-circley[0.01]) is the product of the three quantities.
Include spaces there if you wish, but they're not needed.

Seventh, you seem to be making more work than necessary -- introducing
more names than really needed, and breaking up things into too many
little pieces.  Why not something like the following.  I'll leave out
the factor involving g; since it's a constant, you can obviously just
pull out 1/Sqrt[2g] from the integral.

{x[t_], y[t_]} = 13 (1 - {Sin[t], Cos[t]})

Integrate[ Sqrt[x'[t]^2 + y'[t]^2]/Sqrt[y[t] - y[0.01]],
{t, 0.01, Pi/2}]

Eighth, either I made a mistake above or you have something wrong in
your model, as the result of that integral is complex.

On 2/15/2010 5:47 AM, bwalker at musings.com wrote:
> I am trying to determine the time to travel a circular path. This path is on a
> circle. It's fairly easy to understand.
>
> But, I can't seem to figure out why this is failing.
>
> (* define my parametrizations *)
> circlex[t_]:=13+13*Sin[t+pi];
> circley[t_]:=13+13*Cos[t+pi];
>
> (* the derivatives *)
> dcirx[t_]:=D[circlex[t],t];
> dciry[t_]:=D[circley[t],t];
>
>
> (* amount of time needed to travel a circle *)
> Integrate[Sqrt[(dcirx[t])^2+(dciry[t])^2]/Sqrt[2*g*(circley[time0]-
> circley[t])], {t, 0.01, pi/2}]
>
> I get a negative value for the time. This can't be right..
>
> Any help is much appreciated!!
>
> Thanks.
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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