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Nodimo

The main purpose of Nodimo is to transform a dimensional relationship between variables into a nondimensional one. The variables are gathered in nondimensional groups such that the number of groups is lower than the number of variables. The resulting nondimensional model is, at the same time, a generalization and simplification of the dimensional model.

Nodimo supports any number of dimensions and variables. It can be used for applications in science, engineering, economics and finance. The resulting nondimensional groups can be used as the basis for further studies in similarity and model testing.

Installation

Nodimo and its dependencies (numpy and sympy) are installed by:

pip install nodimo

Alternatively, Nodimo and dependencies can be installed via conda:

conda install nodimo --channel rodrigopcastro018

When running Nodimo on the terminal, make sure that the terminal supports Unicode characters. For the best experience, it is recommended the use of jupyter notebook.

Getting started

Basic example

• Simple pendulum

The nondimensional model for the pendulum's period T as a function of the other variables is built and displayed as:

from nodimo import Variable, NonDimensionalModel

T = Variable('T', mass=0, length=0, time=1, dependent=True)  # period
L = Variable('L', mass=0, length=1, time=0, scaling=True)    # length
m = Variable('m', mass=1, length=0, time=0)                  # mass
g = Variable('g', mass=0, length=1, time=-2, scaling=True)   # gravity
t0 = Variable('theta_0')                                     # initial angle

ndmodel = NonDimensionalModel(T, L, m, g, t0)
ndmodel.show()

And the result is:

$$\displaystyle \frac{T g^{\frac{1}{2}}}{L^{\frac{1}{2}}} = \Pi{\left(\theta_{0} \right)}$$

For more applications and functionalities, check the documentation.

Aknowledgements