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Nodimo

The main purpose of Nodimo is to transform a dimensional relationship between quantities into a dimensionless one. This is done by grouping dimensional quantities into dimensionless products in such a way that the resulting number of products is always lower than or equal to the starting number of quantities. Therefore, the ensuing dimensionless model is, at the same time, a generalization and simplification of the dimensional model.

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

Notes

• The use of Nodimo requires basic knowledge of dimensional analysis, specially on choosing the appropriate set of scaling parameters and indentifying established dimensionless groups.

• It is recommended the use of jupyter notebook for a better displaying of the results.

Installation

Via PyPI, Nodimo is installed by:

pip install nodimo

Alternatively, via Anaconda:

conda install nodimo

Getting started

Basic example

• Simple pendulum

The dimensionless relation between the pendulum's period T and the other quantities presented in the figure above is built and displayed as:

from nodimo import Quantity, Model

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

model = Model(T, L, m, g, t0)
model.show()

And the result is:

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

For more applications and functionalities, check the documentation.