need help determined time to travel a path
in [Mathematica]
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From: bwalker on 15 Feb 2010 05:47 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. Brad Walker
From: Murray Eisenberg on 16 Feb 2010 03:51 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 in your code. Third, your Integrate uses time0, but no time0 has been defined anywhere in your code. 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(a)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. > > Brad Walker > -- Murray Eisenberg murray(a)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
From: Narasimham on 16 Feb 2010 03:50 You assumed that a frictionless particle rotates with uniform angular velocity in the x - y vertical plane under action of gravity, leading to unnatural results. Also value of acceleration due to gravity is to be supplied, pi should be Pi and quantities under radical sign to be checked positive. On Feb 15, 3:47 pm, "bwal...(a)musings.com" <brad2...(a)gmail.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. > > Brad Walker
From: Brad Walker on 16 Feb 2010 03:53 g = 9.81 and time0 = 0 Yea, I guess pi should be capitalized. But, this is what happens when one cuts and paste and it's 11:30 pm.. Thanks for any help. -brad w. On Mon, Feb 15, 2010 at 10:16 AM, Tomas Garza <tgarza10(a)msn.com> wrote: > What is g? What is time0? Also, pi should be capitalized (pi). > > Tomas > >> Date: Mon, 15 Feb 2010 05:47:53 -0500 >> From: brad2000(a)gmail.com >> Subject: need help determined time to travel a path >> To: mathgroup(a)smc.vnet.net >> >> 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. >> >> Brad Walker >> >
From: Tomas Garza on 16 Feb 2010 03:54
What is g? What is time0? Also, pi should be capitalized (pi). Tomas > Date: Mon, 15 Feb 2010 05:47:53 -0500 > From: brad2000(a)gmail.com > Subject: need help determined time to travel a path > To: mathgroup(a)smc.vnet.net > > 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. > > Brad Walker > |