adding new physics algorithm: center of mass

physics/center_of_mass.py

@@ -0,0 +1,95 @@
+"""
+Calculating the center of mass for a discrete system of particles,
+given their positions and masses.
+
+Description:
+
+In physics, the center of mass of a distribution of mass in space
+(sometimes referred to as the barycenter or balance point) is the
+unique point at any given time where the weighted relative position
+of the distributed mass sums to zero. This is the point to which a
+force may be applied to cause a linear acceleration without an angular acceleration.
+Calculations in mechanics are often simplified when formulated with respect to
+the center of mass. It is a hypothetical point where the entire mass of an object
+may be assumed to be concentrated to visualise its motion. In other words, the
+center of mass is the particle equivalent of a given object for application of
+Newton's laws of motion.
+
+In the case of a system of particles P_i, i = 1, ..., n , each with mass m_i
+that are located in space with coordinates r_i, i = 1, ..., n , the coordinates
+R of the center of mass correspond to:
+
+R = (Σ(mi * ri) / Σ(mi))
+
+Reference: https://en.wikipedia.org/wiki/Center_of_mass#:~:text=The%20center%20of%20mass%20is%20the%20unique%20point%20at%20the,distribution%20of%20mass%20in%20space.
+
+"""
+
+
+def center_of_mass(
+    particles: list[tuple[float, float, float, float]]
+) -> tuple[float, float, float]:
+    """
+    Input Parameters
+    ----------------
+    particles (List[Tuple[float, float, float, float]]):
+    A list of particles where each particle is a tuple with it´s (x, y, z)
+    position and it´s mass.
+
+    Returns
+    -------
+    Tuple[float, float, float]:
+    A tuple with de coordinates of the center of mass (Xcm, Ycm, Zcm)
+    rounded to two decimal places.
+
+    Examples
+    --------
+
+    >>> center_of_mass([(1.5, 4, 3.4, 4), (5, 6.8, 7, 8.1), (9.4, 10.1, 11.6, 12.9)])
+    (6.71, 8.05, 8.8)
+
+
+    >>> center_of_mass([(1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12)])
+    (6.33, 7.33, 8.33)
+
+    >>> center_of_mass([(1, 2, 3, -4), (5, 6, 7, 8), (9, 10, 11, 12)])
+    Traceback (most recent call last):
+        ...
+    ValueError: Mass of all particles must be greater than 0
+
+    >>> center_of_mass([(1, 2, 3, 0), (5, 6, 7, 8), (9, 10, 11, 12)])
+    Traceback (most recent call last):
+        ...
+    ValueError: Mass of all particles must be greater than 0
+
+    >>> center_of_mass([])
+    Traceback (most recent call last):
+        ...
+    ValueError: No particles provided
+
+    """
+    if not particles:
+        raise ValueError("No particles provided")
+
+    for particle in particles:
+        if particle[3] <= 0:
+            raise ValueError("Mass of all particles must be greater than 0")
+
+    total_mass = sum(particle[3] for particle in particles)
+
+    center_of_mass_x = round(
+        sum(particle[0] * particle[3] for particle in particles) / total_mass, 2
+    )
+    center_of_mass_y = round(
+        sum(particle[1] * particle[3] for particle in particles) / total_mass, 2
+    )
+    center_of_mass_z = round(
+        sum(particle[2] * particle[3] for particle in particles) / total_mass, 2
+    )
+    return (center_of_mass_x, center_of_mass_y, center_of_mass_z)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()