View Full Version : laplace transforms
has any body ever did a calculated model of a potential hike using laplace transforms:cool: neo
rambunny
05-26-2005, 02:30
What the hey! Are you an engineer or something-hike don't analaze don't check milage-sleep under the stars where you drop. It's the journey!!!!
Stoker53
05-26-2005, 05:29
What the hey! Are you an engineer or something-hike don't analaze don't check milage-sleep under the stars where you drop. It's the journey!!!!
Perhaps Neo's journey is different from yours?:D
Hmmm...
So what exactly would you take the LaPlace transform of? I have to assume it would be something in the time domain. Perhaps velocity?
Or were you implying you would be calculating the gravitational potential of a hike over some distance or time?
Either way, I think the answer is a resounding NO. But if someone can spend their time using a large fluid dynamic finite element model to determine exactly why the shower curtain tends to billow inward in the shower (http://www.umass.edu/newsoffice/archive/2001/070901shower.html), I'd say go for it. Heck, publish the results.
laplace transforms
http://ccrma.stanford.edu/~jos/filters/Laplace_Transform_Analysis.html
:cool: neo
I thought "The Place" had transformed!
By the way, what is that mathematical formula representing?
The Laplace transform transforms a real-valued function into a function of a complex variable.
In engineering Laplace transforms allow you to take differential equation in the time domain and transform it into an algebraic equation in the Laplace domain. All of this is of course subject to certian conditions. The function must be linear (exhibits superposition and homogeneity).
In my field this is often done to make solving the equation much easier. Also plotting the results in the laplace domain often makes it much easier to analyze dynamic systems (vibration and control theory).
Not LaPlace transforms, but there's an old thread (under general AT polls) here about apparent pack weight vs hiking time where I thought about mathematical relationships in hiking. I was going to construct functional relationships between apparent pack weight and various independent variables and publish in the Journal of Irreproducable Results. Here's a repeat of my idea from that thread:
.............
This poll was inspired by my 2 week hike of Vermont in 2001 with a load that was too heavy and a pack that didn't support it well. I began to think of all the variables that could affect my perceived pack weight (time of day, temperature, trail grade, trail condition, time since rest stop, time since eating, etc. ) and how they were functionally related to it (linear, log, exponential, power law). Then I thought that maybe I could put all of this into mathematics and publish it in the "Journal of Irreproducable Results". I could graph my actual pack weight and apparent pack weight as a function of time over the course of the 2 week hike, correlate this with a set of independent variables (temperature, trail grade, etc.), and develop the functional relations. Actually, I was going to take the backwards approach of making up appropriate functional relationships first, then calculation apparent pack weight from actual pack weight, and adding random "noise" so that my pseudoscience looked more realistic. Now you know what scientists think about while hiking.
Anyone want to suggest some functional relationships? I'll make you a co-author of the study. I figure that "time since last rest" should be exponential. "Trail grade" should be a 2nd order quadratic because very steep downhills can be as hard as very steep uphills. Rock, you've given me a new independent variable "time since start of hike" - I think it should be an inverse exponential.
Not LaPlace transforms, but there's an old thread (under general AT polls) here about apparent pack weight vs hiking time where I thought about mathematical relationships in hiking. I was going to construct functional relationships between apparent pack weight and various independent variables and publish in the Journal of Irreproducable Results. Here's a repeat of my idea from that thread:
.............
This poll was inspired by my 2 week hike of Vermont in 2001 with a load that was too heavy and a pack that didn't support it well. I began to think of all the variables that could affect my perceived pack weight (time of day, temperature, trail grade, trail condition, time since rest stop, time since eating, etc. ) and how they were functionally related to it (linear, log, exponential, power law). Then I thought that maybe I could put all of this into mathematics and publish it in the "Journal of Irreproducable Results". I could graph my actual pack weight and apparent pack weight as a function of time over the course of the 2 week hike, correlate this with a set of independent variables (temperature, trail grade, etc.), and develop the functional relations. Actually, I was going to take the backwards approach of making up appropriate functional relationships first, then calculation apparent pack weight from actual pack weight, and adding random "noise" so that my pseudoscience looked more realistic. Now you know what scientists think about while hiking.
Anyone want to suggest some functional relationships? I'll make you a co-author of the study. I figure that "time since last rest" should be exponential. "Trail grade" should be a 2nd order quadratic because very steep downhills can be as hard as very steep uphills. Rock, you've given me a new independent variable "time since start of hike" - I think it should be an inverse exponential.
you may want to consider using fourier transforms:cool: neo
you may want to consider using fourier transforms:cool: neo
http://mathworld.wolfram.com/FourierTransform.html
The Cheat
05-26-2005, 12:30
TYOL
Transform Your Own Laplace
Alligator
05-26-2005, 12:30
Time since last rest stop as a sinesoidal relationship, as it will oscillate, along with time since last eating event modeled similarly. You might model grade as absolute value of grade, but this assumes that the subject considers the ups and downs similarly. A quadratic function is a good choice. Also, consider throwing in some categorical variables, like weather for instance.
Pencil Pusher
05-26-2005, 13:00
Geez, now would be a good time to read Rick the Lone Wolf's Boiling Springs entry on this mathematical stuff.
Ford Prefect
05-26-2005, 13:03
Time since last rest stop as a sinesoidal relationship, as it will oscillate, along with time since last eating event modeled similarly. You might model grade as absolute value of grade, but this assumes that the subject considers the ups and downs similarly. A quadratic function is a good choice. Also, consider throwing in some categorical variables, like weather for instance.
Just remember:
L'Hôpital Rule's
:jump
has any body ever did a calculated model of a potential hike using laplace transforms:cool: neo
Why, yes. As a matter of fact, I have. As a public service to the hiking community, I have posted a summary here. (http://www.me.cmu.edu/faculty1/messner/classes/24-451/other/notes/ntltc.gif)
As you can see, this conclusively proves that an extra pound on your feet is, believe it or not, equivalent to removing 3.1415926535 pounds from your pack (assuming, of course, it has an external frame). ;)
Ford Prefect
05-27-2005, 06:59
Why, yes. As a matter of fact, I have. As a public service to the hiking community, I have posted a summary here. (http://www.me.cmu.edu/faculty1/messner/classes/24-451/other/notes/ntltc.gif)
As you can see, this conclusively proves that an extra pound on your feet is, believe it or not, equivalent to removing 3.1415926535 pounds from your pack (assuming, of course, it has an external frame). ;)
All I see is a proof that the area under the curve of a unit impulse is equal to 1. Neo, you can't have your pi and eat it too!
:banana
By the way, what is that mathematical formula representing?
It's the recipe for Krispy Kreme donuts, you silly crustacean. :D
Ford Prefect
05-27-2005, 07:55
It's the recipe for Krispy Kreme donuts, you silly crustacean. :D
Now the secret's out. So much for trying to obfuscate the true and hidden meaning of the sacred, halowed Krispy Things with silly mathematical blather ...
Stoker53
05-27-2005, 07:58
This thread has me totally lost and ROTFLMAO.:clap
Moon Monster
05-28-2005, 11:50
When in doubt, get a French Mathematician!
flyfisher
05-29-2005, 09:18
http://mathworld.wolfram.com/FourierTransform.html
A fourier transform would be a hard way to get an answer to a question which is actually asked occasionally... In this context, it would be something like looking at the number of days in which the hiker hiked a certain number of miles.
One time domain view of a hike would be to look at each day's mileage a la trail journals. One frequency domain analysis would be to to tablulate how many days were 0 mile days, how many were 1 mile days, how many were 2 mile days....
However I really had to grin when I saw the topic!
It took me 6 months of my Electrical Engineering master's to conceptulise what a Fourier Transform was. Once the idea stuck, it became a reasonably handy tool for thinking.
There's no doubt about it: LaPlace was an arrogant arrogant guy. A giant equation for modeling the entire Universe? He said it, not me. Crazy Leibnizian philosophy: calculemus! No need for that kind of stuff on the trail (and with quantum mechanics in high gear, it couldn't be done anyway). It's more fun to analyze the hike after the fact, anyway.
Sorry to post twice here; I'll try hard not to do it again. Anyway, as long as we have guys doing Fourier Transforms, why don't we do FFTs and derive pi to many places after the decimal? I mean, imagine the untapped computing power of those brains of the (non-altered-state) thru-hikers!
atraildreamer
05-20-2006, 02:32
The Laplace transform transforms a real-valued function into a function of a complex variable.
In engineering Laplace transforms allow you to take differential equation in the time domain and transform it into an algebraic equation in the Laplace domain. All of this is of course subject to certian conditions. The function must be linear (exhibits superposition and homogeneity).
In my field this is often done to make solving the equation much easier. Also plotting the results in the laplace domain often makes it much easier to analyze dynamic systems (vibration and control theory).
David Krumholtz and "NUMB3RS" are looking for you! :eek:
Laplace Transform Yikes. I thought I left that behind in Sophomore year of college in my systems 1 & 2 class. I think I'm going to be sick
Dances with Mice
05-20-2006, 12:03
Laplace Transform Yikes. I thought I left that behind in Sophomore year of college in my systems 1 & 2 class. I think I'm going to be sickThe philosopher Geo. Carlin once considered offering a continuing education course in what you remember from college 20 years after graduating. It would necessarily be a short course.
All I remember are Lip****z (http://arxiv.org/abs/math.DG/0501027) constants. Can't remember a single thing about them, but I do remember that name. Funny how the auto-censor picked that up, isn't it?
But I'll confess that I use Fourier Transforms (http://www.forumsci.co.il/HPLC/FTIR_Process.GIF)every day.
I also have a prepared lecture which clearly demonstrate the wave / particle nature of the electromagnetic spectrum and in particular the operating principles of infrared and ultraviolet analytical detectors using juggling. You get the dough, I'll do the show.
So, How has "The Place" changed. I kinda' liked it like it was. ;)
Hacksaw
betic4lyf
05-20-2006, 14:25
uggh
just finnished my calc class in high school, and i thought i was a calc king. all those formulas, and even more ugly symbols, like the delta over the equals sine. gross.
hey guess what?
e^(i(pi))-1=0
the proof involves taylor series and pain
baerbelleksa
05-22-2006, 23:18
for some reason as i keep seeing this thread title, i keep thinking it says 'lapdance.'
:confused: :confused: :confused:
My head freaking hurts just from reading this. I first thought someone was referring top "The Place". I was sadly mistaken.
I think I'll go read about crotch rot instead.:o
Gray Blazer
05-24-2006, 07:22
for some reason as i keep seeing this thread title, i keep thinking it says 'lapdance.'
Great minds think alike. Obviously these guys are too smart for me. See you at the club!:rolleyes:
for some reason as i keep seeing this thread title, i keep thinking it says 'lapdance.'
http://www.sosmath.com/diffeq/laplace/basic/img2.gif
:D is this a lapdance:cool: neo
Gray Blazer
05-24-2006, 10:19
http://www.sosmath.com/diffeq/laplace/basic/img2.gif
:D is this a lapdance:cool: neo
Doesn't work the same for me. BTW, Neo, good threads lately and I'm not talking about your clothes.:rolleyes: