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"""

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)

>>> 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: 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()

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