laplace transforms
has any body ever did a calculated model of a potential hike using laplace transformsneo
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?Originally Posted by rambunny
"In the abundance of water the fool is thirsty."...Bob Marley
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, I'd say go for it. Heck, publish the results.
laplace transforms
http://ccrma.stanford.edu/~jos/filte..._Analysis.html
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.
you may want to consider using fourier transforms
http://mathworld.wolfram.com/FourierTransform.htmlyou may want to consider using fourier transforms
TYOL
Transform Your Own Laplace
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.
Geez, now would be a good time to read Rick the Lone Wolf's Boiling Springs entry on this mathematical stuff.
How many more of our soldiers must die in Iraq?
Just remember:
L'Hôpital Rule's
Why, yes. As a matter of fact, I have. As a public service to the hiking community, I have posted a summary here.has any body ever did a calculated model of a potential hike using laplace transforms
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).
Is that cake? Or pie?
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!Why, yes. As a matter of fact, I have. As a public service to the hiking community, I have posted a summary here.
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).
It's the recipe for Krispy Kreme donuts, you silly crustacean.
'All my lies are always wishes" ~Jeff Tweedy~
Oh no!
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 ...It's the recipe for Krispy Kreme donuts, you silly crustacean.
This thread has me totally lost and ROTFLMAO.
"In the abundance of water the fool is thirsty."...Bob Marley
When in doubt, get a French Mathematician!
Posting Permissions
Reply With Quote
