HP49G+ - strengths and weakneses?
umpt...@gmail.com
I'm trying to get a picture of the strengths and weaknesses of the
HP49G+ re the TI89 before I decide whether to order one.
The main strengths I care about seem to be "better" CAS (but in what
ways?), the equations editor (but could someone tell me briefly what
advantages this has over the TI89 equivalent in practice?). Matrix
crunching speed and SysRL aren't of much concern to me.
Weaknesses seem to be build quality, the fact that equations in the
stack are kept in user-friendly form, and a higher learning curve?
I'm not strongly for or against RPN.
Umm.. the keyboard IS fixed now, right?
Comments?
A.L.
>
>Umm.. the keyboard IS fixed now, right?
>
I will wait one year more.
A.L.
VPN
news:1129314766.9...@g14g2000cwa.googlegroups.com...
> Hi -
>
> I'm trying to get a picture of the strengths and weaknesses of the
> HP49G+ re the TI89 before I decide whether to order one.
>
> The main strengths I care about seem to be "better" CAS (but in what
Then you have to buy them both
as they are strong in different areas of CAS
so there is no clear winner in this category
> ways?), the equations editor (but could someone tell me briefly what
> advantages this has over the TI89 equivalent in practice?). Matrix
> crunching speed and SysRL aren't of much concern to me.
>
> Weaknesses seem to be build quality, the fact that equations in the
> stack are kept in user-friendly form, and a higher learning curve?
>
> I'm not strongly for or against RPN.
>
> Umm.. the keyboard IS fixed now, right?
No!
The TI 89 Ti has still the old TI 89 style
mushy feeling
bad layout
poorly tailorable keyboard
> Comments?
Buy the 49g+
You can speed it up using software only (keeping warranty)
VPN
crawla...@lycos.com
advantages this has over the TI89 equivalent in practice?)."
I don't know what the TI89 "equivalent" is (if you're talking about the
$15 optional thing, I haven't used it) but I think the 49G+'s equation
editor is a great feature and a major advantage over the TI89.
For one thing, the equation editor is useful not only for entry, but
also simply for *looking* at results.
On the TI89, the "pretty print" feature will only display so much
information vertically. If you have compound fractions, or say a 3x3
matrix with symbolic fraction entries, the whole thing won't show, and
you'll have to copy and paste the result to the entry bar, and try to
decode it. It also takes forever to scroll through a long formula on
the TI89, by the way (you can jump to the beginning or the end, but
there's nothing that lets you jump an amount in between).
These are not problems on the 49G+.
Also, of course the equation writer is a godsend for entering complex
formulas. With the TI89, you can be guaranteed to get unpaired
paranthesis fairly frequently. The equation writer is also nice for
when you have a formula with similar parts repeated. For instance, if
you're entering the Fresnel equations for intensity change on
reflection, you can enter the numerator, copy it, and then paste that
in the denominator, and use the cursor to go right to where you need to
change the sign and change it. On the TI89 the problem is that you
can't edit the formula in pretty print; to find the necessary sign
change you'll have to scroll through the formula bar.
As for the CAS, as said, they're difficult to objectively compare. If
we're talking integrals, there are some the TI89 can do that the 49G+
can't, and some the 49G+ can do that the TI89 can't. And usually the
49G+ is faster, but there might be an odd problem that the TI89 can do
faster. Which of those sorts of problems will be the ones you'll
actually need to deal with? Who knows. But I'd say 3 out of 4 times,
the 49G+ is more powerful. While the TI89 will occasionally do
something faster than the 49G+, when the 49G+ is faster, it's often
MUCH faster.
Example, integrating squareroot of tangent of x. The 49G+ does this in
a couple of seconds. I tried this on the TI89, and it ran and ran, for
over 20 minutes, before I finally cancelled the operation to save the
batteries. I later tried it on a TI89 emulator that ran at a higher
speed, and it did manage to solve it.
(On the other hand, if you do the first substitution, z = tan(x), and
get squareroot(z)/(1+z^2), the TI89 will do that integral in seconds)
Another example, integrals of the form 1/(x^n-1).
If a human was solving this problem, the steps would be obvious:
Factor the denominator as x minus the various nth roots of 1, then use
partial fractions.
Well, in exact mode, the 49G+ can't do that integral if n = 5 or more.
The TI89 can. An advantage for the TI89?
Well, maybe. The 49G+ can still do those integrals, but it needs to be
in approximate mode, because it factors the denominator numerically.
I've only tried it up to n = 11, but it solves that just about
instantly.
On the other hand, the TI89 can do it exactly for n = 7, but it takes
FOREVER. I don't know if a real TI89 could do it before the batteries
would run out. I tried it again on an emulator running at faster
speed, and after leaving it all night it had the answer in the morning.
If you'd hope you could speed the TI89 up by doing it approximately,
you're out of luck. It won't do anything with those integrals in
approx. mode.
Well, it's easy to go on and on with comparisons. I've been working
with some matrices lately, and it seems the TI89 can take
transcendental functions of matrices, but can only do that -- or find
eigenvalues or eigenvectors -- approximately with numerical data.
The 49G+ can't take transcendental functions of matrices, but it can
find eigenvalues and -vectors of symbolic matrices. (Using those
functions, you should be able to write a little program to use
functions on the matrices)
Despite that this post probably seems excessively biased towards the
49G+, I still think the TI89 is a great calculator.
My general guideline for a recommendation would be that it depends on
what you want. If you want the calculator that's easier to use, that'd
probably be the TI89. It automatically simplifies expressions, which
can be annoying if don't want that, but a great time saver if you do.
If you want sheer power, go with the 49G+. I think that eventually the
49G+'s sheer power will eventually allow it to make up for (with
programming or user knowledge) any relative weaknesses it may have to
the TI89 (as in the matrix example above).
I think the 49G+ is for those who are a little more serious about
science and math, while the TI89 is more for people who don't want to
need to invest as much time into learning a calculator.
VPN
news:1129351294.3...@f14g2000cwb.googlegroups.com...
X
> The 49G+ can't take transcendental functions of matrices
crawla...@lycos.com
MAP takes the function of each individual term, not of the matrix
itself.
Example, using MAP to apply the exponential function to the 2x2
identity matrix gives
[e,1]
[1,e]
While really the exponential function of the 2x2 identity should be
[e,0]
[0,e]
crawla...@lycos.com
the exponential function to a 2x2 matrix:
<< EGV V-> EXP SWAP EXP SWAP ->V2 2 DIAG-> SWAP DUP UNROT INV * * >>
VPN
Google anyone not as lazy?
VPN
<crawla...@lycos.com> wrote in message
news:1129386175.9...@g14g2000cwa.googlegroups.com...
VPN
<crawla...@lycos.com> wrote in message
news:1129388458.4...@g49g2000cwa.googlegroups.com...
crawla...@lycos.com
can do it on its own.
You just need to use DIAGMAP rather than simply MAP.
I'll probably be learning more about this calculator 10 years from now.
Virgil
"VPN" <DROP...@dlc.fi> wrote:
MAP won't allow you to get the equivalent to 'EXP(M)' where M is a
square matrix, which is NOT the same as taking EXP of every entry in the
matrix.
One definition of EXP(M), for an arbitrary square matrix M is
Sum(j=0..+oo,M^j/(j!)),
where M^0 is the appropriate identity matrix, and M^j is otherwise the
appropriate power of M.
If the n by n square matrix, M, factors into form INV(U)*D*U, where D is
diagonal and U obviously must be invertible, then EXP(M) = INV(U)*F*U,
where F is the result of \<< \->DIAG \<<EXP\>> MAP n DIAG-> \>>
applied to diagonal D.
This can be done in the HP49 series approximate mode when M has a basis
of eigenvectors.
VPN
"Virgil" <ITSnetNOTcom#vir...@COMCAST.com> wrote in message
news:ITSnetNOTcom%23virgil-903384...@comcast.dca.giganews.com...
Virgil
"VPN" <DROP...@dlc.fi> wrote:
> DIAGMAP
To get the exponential function of a matrix, for most square numerical
matrices in approximate mode, you can use:
\<< EGV \<< EXP \>> MAP DUP SIZE EVAL DIAG\-> OVER / * \>>
VPN
X
> To get the exponential function of a matrix, for most square numerical
> matrices in approximate mode, you can use:
>
> \<< EGV \<< EXP \>> MAP DUP SIZE EVAL DIAG\-> OVER / * \>>
Thanks!
I think I'm slowly getting it
I wonder if in the future there are any math developers @ HPQ
There are still some functionality missing
Like having full trancen-dental care 4 [ [ ] ]
VPN
Joe Horn
> I wonder if in the future there are any math developers @ HPQ
> There are still some functionality missing
> Like having full trancen-dental care 4 [ [ ] ]
Another nice thing would be for it to get the right answer for
EULER(1). EULER(x) = DEGREE(CYCLOTOMIC(x)), so EULER(1) should return
1, not 0 as it always has.
-jkh-
Virgil
"VPN" <DROP...@dlc.fi> wrote:
Correction! In program above, replace "/" by "INV *"
Corrected program is:
\<< EGV \<< EXP \>> MAP DUP SIZE EVAL DIAG\-> OVER INV * * \>>
^^^^^
NOTE
L.A.
Not Good.
Your knowlege of mathematics should
dictate what you understand about the calculator.
Such operating characteristics are not very useful.
-and with a fair manual basicly omitted;
The Hewlett-Packard becomes a looser.
I'd rather work to follow transistor numerical model designations.
L.A.
flon...@longship.net
The HP has RPN. The TI doesn't. With the rest being an approximate
wash, the HP wins hands down.
Bhuvanesh
The TI also has RPN. There is a free add-on RPN interface, and RPN is
used under the hood. The rest of your comment is too vague to reply to
:-)
Bhuvanesh.
A.L.
>One big difference.
>
>The HP has RPN. The TI doesn't.
Who cares?...
By the way, there is pretty good software that converts ti89 into RPN
calculator (for these mentaly challenged who cannot understand what
left and right brackets are for):
http://www.paxm.org/symbulator/download/rpn.html
A.L.
Marcin Witek
> By the way, there is pretty good software that converts ti89 into RPN
> calculator (for these mentaly challenged who cannot understand what
> left and right brackets are for):
>
> http://www.paxm.org/symbulator/download/rpn.html
But it crashes on TI-89 Titanium (AMS 3.10). Is there any way to get it
working?
Wit
umpt...@gmail.com
crawla...@lycos.com wrote:
> I think the 49G+ is for those who are a little more serious about
> science and math, while the TI89 is more for people who don't want to
> need to invest as much time into learning a calculator.
Thank you, that's a great response.
Greg M.
Yes. :)
I actually have used such a setup since about February. It works well. The
only thing that seems broken is the diamond+enter for approximation. Just
setup a downarrow key combination instead.
If you don't want to read the ramblings that follow, how to do it can be
summed up in two words:
HW3Patch. GhostBuster.
I apologize if my instructions are too verbose. Since I have no idea what
you have/haven't tried, I'm going to explain what you would do if you had
just taken your calculator out of the box. Some of this may not need to be
done if it has already been done on your calc.
Please backup first! Any mistakes either on my part or your part could
render your ram cleared. You may need to use 2nd+left+right+on to reset the
ram if something goes wrong.
You will need to download the following:
HW3Patch: http://www.tigen.org/kevin.kofler/ti89prog.htm#hw3patch
GhostBuster: http://www.tigen.org/kevin.kofler/ti89prog.htm#ghostb
RPN: http://www.paxm.org/symbulator/download/rpn.html
And, (optionally, but highly recommended):
KerNO (lightweight kernel which intercepts most crashes):
http://calc.gregd.org/download.php?explain=1&what=kerno
Now that you have all that, you will need to do the following:
1) Unzip HW3Patch and send hw3patch.89z to your calculator. Run it via
"hw3patch()".
2) Unzip GhostBuster and send ghostb.89z to your calculator.
3) Unzip the rpn distribution. Send rpn.89z and rpn_202.89z to your
calculator. Do /not/ launch them now. If at all possible, don't archive
them yet.
4) on the calculator, run: ghostb("rpn",""). You should see in the status
bar: "Patches applied: 4".
5) on the calculator, run: ghostb("rpn_202",""). You should see in the
status bar: "Patches applied: 3"
At this point, rpn should function correctly. I would recommend putting it
in a kbdprgm (read the rpn manual for more info).
However, it is highly recommended that you use KerNO to provide some
protection against your calculator crashing.
You should also be able to move everything but rpn_202 out of the main
folder. You may need to create a "rpn" folder for rpn to function properly.
KerNO will have to be reinstalled whenever you clear your ram.
HW3Patch will only need to be reinstalled next time you perform a flash
upgrade.
As far as actually using rpn, my suggestion would be to really read the
manual. twice. three times. maybe four? There are a lot of hidden features,
any of which may greatly help. But, I digress -- this /is/ comp.sys.hp48,
not some TI-89 mailing list. I'd be happy to continue the discussion via
email. :)
>
> Wit
Greg M.
PS: For a great equation writer, consider "Hail Expression Writer",
available here: http://www.stearley.org/calc.html
If you would like to be able to start it with some unused key combination
(like alpha+enter), try out "shortcut", available from the same place.
JAM
Just recently I was trying to solve engineering problem related to the the
beam that is rigidly mounted in one end and loaded with a constant bending
moment on the other end. Such spring (assuming constant section) bends such
that the bended shape is a piece of the arc. The goal was to find out the
trajectory of the free end of the beam (simple) and then to establish radius
of the curvature of that trajectory when the spring is straight in order to
use such approximation later in the kinematic model that uses rigid links.
The math model assumed that the spring is of a unit length. It is rigidly
mounted at (0,0) and it's free end is at (1,0) when not loaded.
When the spring is loaded, it takes the shape of some arc of a radius R
where the center of the arc is at the point (0,R) and the pie section
created by such arc has angle t.
This allows to establish the parametric equations of the free end of the
spring:
x(t) = R*sin(t)
y(t) = R(1-cos(t))
and knowing that the spring is of a unit length (and the length does not
change) the third equation:
R*t = 1
Substituting R from the above equation gives desired trajectory parametric
set of equations, where t=0 represents straight , not loaded spring but to
get x and y at 0 one must use limit for t->0
x(t) = sin(t)/t
y(t) = (1-cos(t))/t
To this point it was simple. Now using the formula for the radius of
curvature I can calculate the radius:
r = |((dx/dt)^2 + (dy/dt)^2)^(3/2)/((dx/dt)*(d2y/dt2)-(dy/dt)*(d2x/dt2))|
where df/dt is a first degree deriviative and d2f/dt2 is a second degree. I
originally started this with my HP49g+. The outcome was:
X = sin(t)/t
Y=(1-cos(t))/t
1'st degree deriviatives:
XP1 = -(sin(t)-cos(t)*t)/t^2
YP1 = -(1-cos(t)-sin(t)*t)/t^2
2'nd degree deriviatives
XP2 = (2*sin(t)-2*cos(t)*t-sin(t)*t^2)/t^3
YP2 = (2-2*cos(t)-2*sin(t)*t+cos(t)*t^2)/t^3
Radius of curvature (absolute value ommited for simplicity)
r(t) = Simplify((xp1^2+yp1^2)^(3/2)/(xp1*yp2-xp2*yp1))
which produced (after many seconds of waiting) monsterous formula that is
just impractical for me to reproduce it here. Anyway, the formula is of a
form of f(t)/g(t) where both functions produce 0/0 for t=0. This does not
allow to calculate radius of a curvature directly but requires to use limit
functionality. The final step was:
limit r(t) for t->0 which on a HP49G+ after many seconds of waiting produces
the following output:
- First you see the following message: "Got expr. indep of var"
- Then you press OK to get rid of the (have no clue what it means) message
and you get nice looking "?"
At this point I my thought was, that the formula for r(t) was really long
and probably very difficult to calculate limit and I decided to try to find
it numerically by substituting smaller and smaller values for t.
I started with:
t = 0.1 produced: r(0.1) = 0.871...
t = 0.01 produced: r(0.01) = ERROR EVAL inifinite result.
I just gave up. I knew, that for 0.01 there should be a solution that is
finite. Then after a few days I dusted off my old TI92+. I had to even
replace batteries because the old ones just died over time.
My TI92+ produced:
X=sin(t)/t
Y=(1-cos(t))/t
XP1=cos(t)/t-sin(t)/t^2
YP1=(cos(t)+t*sin(t)-1)/t^2
XP2=(2/t^3-1/t)*sin(t)-2*cos(t)/t^2
YP2=((t^2-2)*cos(t)-2*(t*sin(t)-1))/t^3
r(t)=(-2*cos(t)-2*t*sin(t)+t^2+2)^(3/2)/(t^3*(t*(cos(t))^2+sin(t)*(t*sin(t)-1)))
All those steps where almost as fast as I could type. There was no waiting
anywhere for a calculator to simplify internally. Already here TI92+
produced formula that is relatively short and readable. But that would not
impress me yet that much. TI was known to produce nicer looking simplified
formulas, but that was sometimes considered bad for mathematical purists. I
now decided to test the formulat for the same numerical values as I did for
HP49g+. It just did not occured to me to use limit function at this point.
I've got:
t=0.1 produced r(t) = 0.74975....
t = 0.01 produced r(t) = 0.75000....
which seemed consistent, different from HP, but at least consistent. Then I
decided to use limit function.
limit(r,t,0,1) produced exact solution of 3/4
Now I had no clue, which one was right. It seem at the time, that either HP
or TI failed to produce the right formula. I wasn't sure if I could trust TI
despite producing output without the error. HP always had my biased
admiration in the past. I fired my Mathematica on a PC and got:
x[t_]=Sin[t]/t
y[t_]=(1-Cos[t])/t
x1[t_]=Cos[t]/t-Sin[t]/t^2
y1[t_]=-(1-Cos[t])/t^2+Sin[t]/t
x2[t_]=-2*Cos[2]/t^2+2*Sin[t]/t^3-Sin[t]/t
y2[t_]=2*(1-Cos[t])/t^3+Cos[t]/t-2*Sin[t]/t^2
r(t_)=(t^3*((2+t^2-2*Cos[t]-2*t*Sin[t])/t^4)^(3/2))/(t-Sin[t])
The look of the simplified r(t) was here definitevely the best for my eyes,
but the TI92+ was still OK to read. What you expect from the software that
is several times more expensive than the calculator. Only HP49 failed to
produce relatively readable ouptut even when simplified. But the last
operation was the key.
Limit[r[t],t->0] produced 3/4 exactly the same as TI92+
So it produced my original goal of the exercise since I generally trust
Mathematica. HP49g+ turned again (I already had similar issues in the past
with other simple engineering problems) incapable to solve problem and
produced algebraic output that failed to calculate even numerical
approximation within a reasonable margin of error.
If only TI could have native RPN, faster matrix and stack programming
similar to HP ...
JAM
John H Meyers
JAM wrote (in a very familiar style, as always :)
[snipped]
But Jacek, as you well know from your long experience
with HP and TI calculators, in the newer HP product line,
"the important thing is to understand what you're doing,
rather than to get the right answer" :)
[plagiarized from:
http://members.aol.com/quentncree/lehrer/newmath.htm]
"I got it from Lobachevsky"
http://members.aol.com/quentncree/lehrer/lobachev.htm
http://members.aol.com/quentncree/lehrer/agnes.htm
If you forgot Lehrer's original tunes, here they are:
http://members.aol.com/quentncree/lehrer
With best wishes for happy automotive engineering.
[r->][OFF]
Raymond Del Tondo
very nice links:-)))
Regards
Raymond
"John H Meyers" <jhme...@miu.edu> schrieb im Newsbeitrag
news:op.sy2bj...@news.cis.dfn.de...
JAM
I guess my frustration just added up finally on this last straw. I have one
of those HP49G+ with miserable keyboards. Prior to the latest software
update it was failing randomly to register some keys. After the update it is
now registering randomly keys as several strokes of the same key. I don't
really know what is worse, fail to register a key or register it as two or
three strokes ?
I have tried different values for keytime but it doesn't seem to help much.
But what frustrated me the most, was, that when the problem, I described,
failed to solve on HP (including numerical approximation, which was failing
too), I thought, that TI will also either fail to solve it or would require
special, time consuming tricks, which probably one could also employ to
solve it on HP. I quit using TI long time ago and forgot it. To my surprise
my dusted off TI solved the issue without any tricks, and also did it so
fast. The real eye opener was the final form of the r(t) formula. On the HP
after applying "EVAL", "SIMPLIFICATION", "COLLECT" and "kitchen sink" the
formula looks as pure, unreadable garbage, that is hard to analyze and
decipher what fails in numerical approximation. The convoluted look of the
formula, which HP used so much time to produce, makes it practically
impossible to decipher and apply your own algebraic skills to find out the
solution that the calculator fails to do. On the contrary, the formula on TI
was elegant, simple to read, short to display in the window, so even if TI
would fail to find limit, it would be so much easier for the user to find
the solution manually. TI formula was almost as good looking as the one
produced by the Mathematica, $2000 software package.
The TI keyboard was such a pleasure to work with when I suddenly switched
from HP to TI. It reminded me how good HP keyboard used to be and how bad
the current product is. I finally realized that I'm hanging on HP mostly
because of admiration for RPN and admiration for the whole HP OS integration
including excellent integration of programming. TI lacks so much in the
beauty of its OS, but when it comes to the algebraic real life work, it just
beats HP over and over again at least in the algebra range that I'm
employing in my work.
JAM
"John H Meyers" <jhme...@miu.edu> wrote in message
news:op.sy2bj...@news.cis.dfn.de...
John H Meyers
> TI lacks so much in the beauty of its OS
Funnily enough, I was just reflecting
that I have not put my attention on these HP products
for any practical result that they give to my life,
but *only* because they reflect some inspiration
in the qualities of human consciousness that they reflect,
from the souls of their designers,
and that they likewise inspire some bit of shared recognition,
from among those who admire them,
of that common inner stuff of which we are all made.
I recall a book called "The Soul of a new Machine"
http://www.amazon.com/gp/product/0316491977
the title of which also conveys the fact
that there is more to what we act for
than any "bean counters" can account for.
Similarly, I find these quotes appealing,
coming from those who are supposedly known
for "objective science," when in fact
nothing but subjectivity exists,
reflecting only what is inside ourselves:
"A mathematician, like a painter or a poet, is a maker of patterns.
If his patterns are more permanent than theirs,
it is because they are made with ideas.
The mathematician's patterns, like the painter's or the poet's,
must be beautiful; the ideas, like the colours or the words,
must fit together in a harmonious way. Beauty is the first test;
there is no permanent place in the world for ugly mathematics."
- G. H. Hardy, "A Mathematician's Apology"
"I do not know what I may appear to the world; but to myself
I seem to have been only like a boy playing on the seashore,
and diverting myself now and then finding a smoother pebble
or a prettier shell than ordinary, whilst the great ocean of truth
lay all undiscovered before me."
- Isaac Newton (1642-1727)
"A human being is part of a whole, called by us the universe,
a part limited in time and space. We experience ourselves,
our thoughts and feelings, as something separate from the rest,
a kind of optical delusion of consciousness. This delusion is
a kind of prison for us, restricting us to our personal desires
and to affection for a few persons nearest to us. Our task
must be to free ourselves from this prison by widening our
circle of compassion to embrace all living creatures,
and the whole of nature in its beauty..."
- Albert Einstein
With best wishes from
http://www.mum.edu
http://www.maharishischooliowa.org
John H Meyers
> I'm hanging on HP mostly because of admiration for RPN
> and admiration for the whole HP OS integration,
> including excellent integration of programming.
> TI lacks so much in the beauty of its OS...
Here's a short quote from a reviewer (Leo Lim)
of Pulitzer Prize winner Tracy Kidder's book
"The Soul Of A New Machine":
"Tells the tale of a bunch of developers who invested
body and soul to the creation of Data General's new machine
only to find out that the world views the finished product
merely as a commodity with a price tag.
Indeed, the soul of the new machine got lost in transit
from the lab to the marketing department."
And that's where it got lost at HP, too.
As well as in the whole wider world.
[r->][OFF]
reth
Marcin Witek
> 4) on the calculator, run: ghostb("rpn",""). You should see in the status
> bar: "Patches applied: 4".
> 5) on the calculator, run: ghostb("rpn_202",""). You should see in the
> status bar: "Patches applied: 3"
Thank You very much! I didn't know about this ghostbuster step. I am using
preos and it is working great now.
> But, I digress -- this /is/ comp.sys.hp48, not some TI-89 mailing list.
> I'd be happy to continue the discussion via email. :)
OK ok! I just want to say thanks! ;)
> PS: For a great equation writer, consider "Hail Expression Writer",
> available here: http://www.stearley.org/calc.html
> If you would like to be able to start it with some unused key combination
> (like alpha+enter), try out "shortcut", available from the same place.
I am using this great program since my first day with TI-89 ;)
Wit
JAM
news:1130157988.4...@g47g2000cwa.googlegroups.com...
> JAM, do you know what logorrhea means?
Lack of arguments ?
JAM
crawla...@lycos.com
To add to the continuing list of comparisons between these two
calculators, today I had the expression come up
(1 + x^2)^(1/6) cos(atan(x)/3) / x^(1/3)
and take the limit as x tends to i.
*Both calculators* gave the wrong result (zero).
They apparently just looked at the first term, which does tend to zero,
not realizing that atan(i) is infinite.
The correct result is
cuberoot(2)/4 * (squareroot(3) + i)
I do think it takes a bit of common (or even extracommon) sense to use
these calculators correctly.
bar...@nospamcomcast.net
> HP49+ generally fails you, when you need it.
>
> Just recently I was trying to solve engineering problem related to the the
> beam that is rigidly mounted in one end and loaded with a constant bending
> moment on the other end.
I don't agree with the problem formulation and here is why.
\|
\| L W
\|
| max tension
\|---------------------------------------------------| neutral
axis
\|---------------------------------------------------|
\|
max compression
\|
Cantilevered end Free end
Free Body Diagram - Point Load Case
Free-body diagram would indicate cantilevered beam, one end; free
other end in bending. Bending moment is the product of a load (point
or uniform) multiplied by a distance. If L is length of beam and w is
uniform load across beam of length = L, bending moment is (L x w) x
L/2. Or if a point load (W) exists at 1,1 then bending moment = LW.
Units for bending moment are foot-lbs. or newton-meters.
Such spring (assuming constant section) bends such
> that the bended shape is a piece of the arc.
Unlikely if beam is of constant cross-section.
The goal was to find out the
> trajectory of the free end of the beam (simple) and then to establish radius
> of the curvature of that trajectory when the spring is straight in order to
> use such approximation later in the kinematic model that uses rigid links.
>
> The math model assumed that the spring is of a unit length. It is rigidly
> mounted at (0,0) and it's free end is at (1,0) when not loaded.
> When the spring is loaded, it takes the shape of some arc of a radius R
> where the center of the arc is at the point (0,R) and the pie section
> created by such arc has angle t.
The bottom of the beam will be have a length less than L (1) while the
top of the beam will be greater than L (1) as the beam section from
top to bottom goes from tension, to neutral, to compression with
maximum strain at the limits. The neutral axis may be close to the
center of the beam, but it depends on the beam shape and material
properties of the beam.
The point where L=1 in the beam section for a given load is at the
neutral axis. Many circles of progressively smaller radii as you move
from top to bottom can be modelled as finite elements or an exact
solution at each point of interest can be obtained.
______ maximum tensile force (longest length, L= 1+tensile
strain)
\
\
\
\ neutral axis (L=1)
\
\
\
_______ maximum compressive force (shortest length, L = 1 -
compression strain)
Beam Section
>
> This allows to establish the parametric equations of the free end of the
> spring:
The equations that follow should be reworked to model the actual beam
load taking into account the beam section and strength properties.
From what I gathered, purpose of this thread was to show that the Ti
could simplify ridiculously complex equations more easily than the
HP49g+ and therefore everyone should run out and grab one at the first
opportunity. Well, please consider first whether it might make more
sense to correctly model the problem using sound engineering
principals, then use the tool that is better suited to help.
John Baranowsky
Somewhere in the USA
--
A.L.
>John
>
>I guess my frustration just added up finally on this last straw. I have one
>of those HP49G+ with miserable keyboards. Prior to the latest software
>update it was failing randomly to register some keys. After the update it is
>now registering randomly keys as several strokes of the same key. I don't
>really know what is worse, fail to register a key or register it as two or
>three strokes ?
>I have tried different values for keytime but it doesn't seem to help much.
It seems that this procedure ie equally effectiev as curing AIDS with
cosmetic powder.
A.L.
crawla...@lycos.com
are already built into the 49G+ equation library that comes with ROM
2.00!!