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92 lines
2.6 KiB
Python
92 lines
2.6 KiB
Python
"""
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Checks if a system of forces is in static equilibrium.
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"""
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from __future__ import annotations
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from numpy import array, cos, cross, float64, radians, sin
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from numpy.typing import NDArray
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def polar_force(
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magnitude: float, angle: float, radian_mode: bool = False
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) -> list[float]:
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"""
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Resolves force along rectangular components.
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(force, angle) => (force_x, force_y)
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>>> import math
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>>> force = polar_force(10, 45)
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>>> math.isclose(force[0], 7.071067811865477)
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True
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>>> math.isclose(force[1], 7.0710678118654755)
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True
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>>> polar_force(10, 3.14, radian_mode=True)
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[-9.999987317275396, 0.01592652916486828]
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"""
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if radian_mode:
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return [magnitude * cos(angle), magnitude * sin(angle)]
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return [magnitude * cos(radians(angle)), magnitude * sin(radians(angle))]
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def in_static_equilibrium(
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forces: NDArray[float64], location: NDArray[float64], eps: float = 10**-1
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) -> bool:
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"""
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Check if a system is in equilibrium.
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It takes two numpy.array objects.
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forces ==> [
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[force1_x, force1_y],
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[force2_x, force2_y],
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....]
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location ==> [
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[x1, y1],
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[x2, y2],
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....]
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>>> force = array([[1, 1], [-1, 2]])
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>>> location = array([[1, 0], [10, 0]])
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>>> in_static_equilibrium(force, location)
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False
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"""
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# summation of moments is zero
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moments: NDArray[float64] = cross(location, forces)
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sum_moments: float = sum(moments)
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return abs(sum_moments) < eps
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if __name__ == "__main__":
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# Test to check if it works
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forces = array(
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[
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polar_force(718.4, 180 - 30),
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polar_force(879.54, 45),
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polar_force(100, -90),
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]
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)
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location: NDArray[float64] = array([[0, 0], [0, 0], [0, 0]])
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assert in_static_equilibrium(forces, location)
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# Problem 1 in image_data/2D_problems.jpg
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forces = array(
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[
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polar_force(30 * 9.81, 15),
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polar_force(215, 180 - 45),
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polar_force(264, 90 - 30),
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]
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)
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location = array([[0, 0], [0, 0], [0, 0]])
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assert in_static_equilibrium(forces, location)
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# Problem in image_data/2D_problems_1.jpg
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forces = array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])
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location = array([[0, 0], [6, 0], [10, 0], [12, 0]])
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assert in_static_equilibrium(forces, location)
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import doctest
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doctest.testmod()
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