## Python, , in_static_equilibrium.py

``````"""
Checks if a system of forces is in static equilibrium.
"""
from __future__ import annotations

from numpy import array, cos, cross, ndarray, radians, sin

def polar_force(
magnitude: float, angle: float, radian_mode: bool = False
) -> list[float]:
"""
Resolves force along rectangular components.
(force, angle) => (force_x, force_y)
>>> import math
>>> force = polar_force(10, 45)
>>> math.isclose(force[0], 7.071067811865477)
True
>>> math.isclose(force[1], 7.0710678118654755)
True
[-9.999987317275396, 0.01592652916486828]
"""
return [magnitude * cos(angle), magnitude * sin(angle)]

def in_static_equilibrium(
forces: ndarray, location: ndarray, 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: ndarray = cross(location, forces)
sum_moments: float = sum(moments)
return abs(sum_moments) < eps

if __name__ == "__main__":
# Test to check if it works
forces = array(
[
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()
``````