adding new physics algorithm: center of mass (#10743)

* adding new physics algorithm: center of mass

* Add changes requested by the reviewer

* Add changes requested by the reviewer

* Update center_of_mass.py

* Update center_of_mass.py

---------

Co-authored-by: Christian Clauss <cclauss@me.com>

physics/center_of_mass.py

@@ -0,0 +1,109 @@
+"""
+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 visualize its motion. In other words, the center of mass
+is the particle equivalent of a given object for the 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 corresponds to:
+
+R = (Σ(mi * ri) / Σ(mi))
+
+Reference: https://en.wikipedia.org/wiki/Center_of_mass
+"""
+from collections import namedtuple
+
+Particle = namedtuple("Particle", "x y z mass")  # noqa: PYI024
+Coord3D = namedtuple("Coord3D", "x y z")  # noqa: PYI024
+
+
+def center_of_mass(particles: list[Particle]) -> Coord3D:
+    """
+    Input Parameters
+    ----------------
+    particles: list(Particle):
+    A list of particles where each particle is a tuple with it´s (x, y, z) position and
+    it´s mass.
+
+    Returns
+    -------
+    Coord3D:
+    A tuple with the coordinates of the center of mass (Xcm, Ycm, Zcm) rounded to two
+    decimal places.
+
+    Examples
+    --------
+    >>> center_of_mass([
+    ...     Particle(1.5, 4, 3.4, 4),
+    ...     Particle(5, 6.8, 7, 8.1),
+    ...     Particle(9.4, 10.1, 11.6, 12)
+    ... ])
+    Coord3D(x=6.61, y=7.98, z=8.69)
+
+    >>> center_of_mass([
+    ...     Particle(1, 2, 3, 4),
+    ...     Particle(5, 6, 7, 8),
+    ...     Particle(9, 10, 11, 12)
+    ... ])
+    Coord3D(x=6.33, y=7.33, z=8.33)
+
+    >>> center_of_mass([
+    ...     Particle(1, 2, 3, -4),
+    ...     Particle(5, 6, 7, 8),
+    ...     Particle(9, 10, 11, 12)
+    ... ])
+    Traceback (most recent call last):
+        ...
+    ValueError: Mass of all particles must be greater than 0
+
+    >>> center_of_mass([
+    ...     Particle(1, 2, 3, 0),
+    ...     Particle(5, 6, 7, 8),
+    ...     Particle(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")
+
+    if any(particle.mass <= 0 for particle in particles):
+        raise ValueError("Mass of all particles must be greater than 0")
+
+    total_mass = sum(particle.mass for particle in particles)
+
+    center_of_mass_x = round(
+        sum(particle.x * particle.mass for particle in particles) / total_mass, 2
+    )
+    center_of_mass_y = round(
+        sum(particle.y * particle.mass for particle in particles) / total_mass, 2
+    )
+    center_of_mass_z = round(
+        sum(particle.z * particle.mass for particle in particles) / total_mass, 2
+    )
+    return Coord3D(center_of_mass_x, center_of_mass_y, center_of_mass_z)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()