Campo de momentos de uma força

Visualizer for the moment field of a single force — coursework for Mecânica I (Escola Politécnica da USP). Given a force F applied at a point P, the program draws M(O) = (P − O) ∧ F over sampled poles O and demonstrates that the field is axisymmetric about the line of action of F.

This is the Python reference implementation: an interactive CLI that produces a static PDF report (perspective views plus the two proof sections) and a numerical verification of the axisymmetry.

Setup

python3 -m venv .venv
.venv/bin/pip install -r requirements.txt

Usage

Interactive (asks for P and F in the shell):

.venv/bin/python -m momentfield

Non-interactive:

.venv/bin/python -m momentfield --ponto "1 0 2" --forca "2 1 -1.5" --saida campo_de_momentos.pdf

Run .venv/bin/python -m momentfield --help for the sampling options (number of planes, spacing, angular step, radii, moment drawing scale) and the optional JSON export of the samples.

The output PDF contains:

1. a title page with the input data, the sampling layout, the color legend and the numerical verification results;
2. perspective views of the full field from several observer positions;
3. the section normal to the line of action (single plane of poles — the pinwheel invariant under 60° rotations);
4. the section containing the line of action (moments normal to the page, magnitude linear in the distance to the axis), plus a slightly tilted view of the same data to make the out-of-page vectors visible.

Tests

.venv/bin/python -m pytest tests/

The tests are numerical assertions to machine precision: M · u = 0, |M| = |F| · dist(O, axis), invariance under axial translation, rotational equivariance, sampling layout, and exact round-trip of the JSON contract.