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arithmetic_analysis/static_solver.py

@@ -0,0 +1,81 @@
+"""
+Checks if a system of forces is in static equilibrium.
+
+python/black : true
+flake8 : passed
+mypy : passed
+"""
+
+from numpy import array, cos, sin, radians, cross # type: ignore
+from typing import List
+
+
+def polar_force(
+ magnitude: float, angle: float, radian_mode: bool = False
+) -> List[float]:
+ """
+ Resolves force along rectangular components.
+ (force, angle) => (force_x, force_y)
+ """
+ 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],
+ ....]
+ """
+ # summation of moments is zero
+ moments: array = cross(location, forces)
+ sum_moments: float = sum(moments)
+ return True if (abs(sum_moments) < eps) else False
+
+
+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]])
+
+ status = in_static_equilibrium(forces, location)
+ assert status
+
+ # 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]])
+
+ status = in_static_equilibrium(forces, location)
+ assert status
+
+ # 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]])
+
+ status = in_static_equilibrium(forces, location)
+ assert status