mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 23:11:09 +00:00
96 lines
2.6 KiB
Python
96 lines
2.6 KiB
Python
"""
|
|
Checks if a system of forces is in static equilibrium.
|
|
"""
|
|
|
|
from __future__ import annotations
|
|
|
|
from numpy import array, cos, cross, float64, radians, sin
|
|
from numpy.typing import NDArray
|
|
|
|
|
|
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
|
|
>>> force = polar_force(10, 3.14, radian_mode=True)
|
|
>>> math.isclose(force[0], -9.999987317275396)
|
|
True
|
|
>>> math.isclose(force[1], 0.01592652916486828)
|
|
True
|
|
"""
|
|
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[float64], location: NDArray[float64], 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[float64] = cross(location, forces)
|
|
sum_moments: float = sum(moments)
|
|
return bool(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: NDArray[float64] = 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()
|