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https://github.com/cheind/sympy-nondim

Non-dimensionalization of physical equations using sympy.

https://github.com/cheind/sympy-nondim

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Keywords

buckingham non-dimensionalisation pi-theorem rayleigh-algorithm
Last synced: 10 months ago · JSON representation

Repository

Non-dimensionalization of physical equations using sympy.

Basic Info
  • Host: GitHub
  • Owner: cheind
  • License: mit
  • Language: Python
  • Default Branch: develop
  • Homepage:
  • Size: 2.25 MB
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buckingham non-dimensionalisation pi-theorem rayleigh-algorithm
Created over 5 years ago · Last pushed over 5 years ago
Metadata Files
Readme License

README.md

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sympy-nondim

This Python package addresses physical dimensional analysis. In particular, sympy-nondim calculates from an unknown relation of (dimensional) variables, a new relation of (usually fewer) dimensionless variables.

See nondim-sympy.pdf for a detailed introduction.

``` python import sympy from sympy.physics import units

import nondim

Potentially relevent variables

t, m, l, g, theta = sympy.symbols('t m l g theta')

and associated dimensions

dimmap = { t:units.time, m:units.mass, l:units.length, g:units.acceleration, theta:units.Dimension(1) }

Setup an general equation, informing dimensional analysis

of dependent and independent variables.

eq = sympy.Eq(t, sympy.Function('f')(m,l,g,theta))

Perform dimensional analysis which returns a new (reduced)

expr. of dimensionless variables

r = nondim.nondim(eq, dimmap)

print(sympy.latex(r))

\frac{\sqrt{g} t}{\sqrt{l}} = F{\left(\theta \right)}

```

The method implemented in this library is based on the Buckingham-Pi theorem and the Rayleigh algorithm as explained in (Szirtes 2007). The method implemented here frames the problem in linear algebra terms, see buckpi.py for details.

In case you are interested in solving for particular dimensions you might be interested in py-dimensional-analysis.

References

Lemons, Don S. 2017. *A Student’s Guide to Dimensional Analysis*. Cambridge University Press.
Santiago, Juan G. 2019. *A First Course in Dimensional Analysis: Simplifying Complex Phenomena Using Physical Insight*. MIT Press.
Schetz, Joseph A, and Allen E Fuhs. 1999. *Fundamentals of Fluid Mechanics*. John Wiley & Sons.
Sonin, Ain A. 2001. “Dimensional Analysis.” Technical report, Massachusetts Institute of Technology. .
Szirtes, Thomas. 2007. *Applied Dimensional Analysis and Modeling*. Butterworth-Heinemann.

Owner

  • Name: Christoph Heindl
  • Login: cheind
  • Kind: user
  • Location: Austrian area

I am a computer scientist working at the interface of perception, robotics and deep learning.

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Dependencies

requirements.txt pypi
  • sympy >=1.7.1