Python/arithmetic_analysis/in_static_equilibrium.py

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"""
Checks if a system of forces is in static equilibrium.
python/black : true
flake8 : passed
mypy : passed
"""
from typing import List
from numpy import array, cos, cross, radians, sin # type: ignore
def polar_force(
magnitude: float, angle: float, radian_mode: bool = False
) -> List[float]:
"""
Resolves force along rectangular components.
(force, angle) => (force_x, force_y)
>>> polar_force(10, 45)
[7.0710678118654755, 7.071067811865475]
>>> polar_force(10, 3.14, radian_mode=True)
[-9.999987317275394, 0.01592652916486828]
"""
if radian_mode:
return [magnitude * cos(angle), magnitude * sin(angle)]
return [magnitude * cos(radians(angle)), magnitude * sin(radians(angle))]
def in_static_equilibrium(
forces: array, location: array, eps: float = 10 ** -1
) -> bool:
"""
Check if a system is in equilibrium.
It takes two numpy.array objects.
forces ==> [
[force1_x, force1_y],
[force2_x, force2_y],
....]
location ==> [
[x1, y1],
[x2, y2],
....]
>>> force = array([[1, 1], [-1, 2]])
>>> location = array([[1, 0], [10, 0]])
>>> in_static_equilibrium(force, location)
False
"""
# summation of moments is zero
moments: array = cross(location, forces)
sum_moments: float = sum(moments)
return abs(sum_moments) < eps
if __name__ == "__main__":
# Test to check if it works
forces = array(
2019-10-05 05:14:13 +00:00
[polar_force(718.4, 180 - 30), polar_force(879.54, 45), polar_force(100, -90)]
)
location = array([[0, 0], [0, 0], [0, 0]])
assert in_static_equilibrium(forces, location)
# Problem 1 in image_data/2D_problems.jpg
forces = array(
[
polar_force(30 * 9.81, 15),
polar_force(215, 180 - 45),
polar_force(264, 90 - 30),
]
)
location = array([[0, 0], [0, 0], [0, 0]])
assert in_static_equilibrium(forces, location)
# Problem in image_data/2D_problems_1.jpg
forces = array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])
location = array([[0, 0], [6, 0], [10, 0], [12, 0]])
assert in_static_equilibrium(forces, location)
import doctest
doctest.testmod()