Laplace Numerical Inversion vs. Numerical Integration: Rumbe in the Time-Domain
Author
Most rigid-body dynamics system seem to rely upon finding the solution to the equations of motion to a system in the time-domain through numerical integration (Euler, Runge-Kutta, etc...) but due to the inherently iterative nature of the algorithms, it can be a source of much slow down when large numbers of objects are present.
I've been investigating the potential for solving the equations of motion numerically in the s-domain using Laplace transforms, however I can't find any references comparing the stability, accuracy and computation times of Laplace numerical inverse transforms against standard numerical techniques.
Has anyone come across any articles or resources profiling both solution mechanisms for similar problems?
Adam
no i never heard of that approach applied to numerical problems. i wouldnt even have a clue what it would be like if it is possible at all, but it certainly does sound interesting. please let me know if you find out more.
Author
Thanks, I've gathered a number of research papers together now, and I'm going to trawl through them and produce some basic code implementations that I can profile against "traditional" numerical techniques.
Quote:Original post by BrianTheLlama
Thanks, I've gathered a number of research papers together now, and I'm going to trawl through them and produce some basic code implementations that I can profile against "traditional" numerical techniques.
what did you find?
i believe modal decomposition is quite expensive, so it can only be done on semi-rigid bodies as a preprocessing step, because changing geometry requires recalculation.
did you find any other methods?
[Edited by - Eelco on June 12, 2005 6:47:41 AM]
Quote:Original post by BrianTheLlama
Thanks, I've gathered a number of research papers together now, and I'm going to trawl through them and produce some basic code implementations that I can profile against "traditional" numerical techniques.
You can probably find most of those answers in the docs for mathlab or just by running simple tests in mathlab. But that requires that you have mathlab though. :)
Author
Laplace transforms are commonly used in control systems, which require knowledge of the equations of motion for the governed mechanical system. These systems are required to operate in real-time, hence my thinking they may be fast enough to construct a simulation with.
I've come across a plethora of research papers that look promising, I haven't got my teeth into them yet but I will attempt to do so during the week and flesh out some formal methodology for building a fast numerical solver.
Fortunately I also have MatLab, but I've never used it for Laplace transforms: I'll do as you suggest and have a dig in the documentation.
Thanks for all your help,
Adam
Edit: If you're interested in having a look yourself, I'll dig out the list of journals and papers I found and post them some time tomorrow.
I've come across a plethora of research papers that look promising, I haven't got my teeth into them yet but I will attempt to do so during the week and flesh out some formal methodology for building a fast numerical solver.
Fortunately I also have MatLab, but I've never used it for Laplace transforms: I'll do as you suggest and have a dig in the documentation.
Thanks for all your help,
Adam
Edit: If you're interested in having a look yourself, I'll dig out the list of journals and papers I found and post them some time tomorrow.
afaik, mathlabs numerical dynamic system stuff (simulink?) doesnt do anything fancy. just old fashioned explicit integration or atleast thats the looks of it.
it can do some more abstract analysis on a system, but i see no evidence it uses any of that to actually advance the whole thing.
it can do some more abstract analysis on a system, but i see no evidence it uses any of that to actually advance the whole thing.
Quote:Original post by Eelco
afaik, mathlabs numerical dynamic system stuff (simulink?) doesnt do anything fancy. just old fashioned explicit integration or atleast thats the looks of it.
it can do some more abstract analysis on a system, but i see no evidence it uses any of that to actually advance the whole thing.
Well, the Laplace translations is probably in a toolbox. It may not be in the most basic Matlab version. But the docs are probably online anyway.
Matlab is perfect for testing numercial models no matter what you are doing.
Matlab may have some core support for the Laplace transform (function call "laplace" and inverse "ilaplace". If not, it is surely in the Control System Toolbox, specifically.
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