Center of mass for a system of particles
========================================

The center of mass (com) of a system of particles is a unique point at any given time where
the sum of weighted relative positions of the distributed mass is zero.

**Links:**

#. `Wikipedia, second formula <https://en.wikipedia.org/wiki/Center_of_mass#A_system_of_particles>`__.

.. py:currentmodule:: symplyphysics.classical_mechanics.kinematics.centers.center_of_mass_for_system_of_particles

.. py:data:: center_of_mass

    Vector of the system's center of mass (COM).

Symbol:
    :code:`r_com`

Latex:
    :math:`{\vec r}_\text{COM}`

Dimension:
    :code:`length`


.. py:data:: position_vector

    Position vector of the :math:`i`-th body. See :attr:`~symplyphysics.symbols.classical_mechanics.distance_to_origin`.

Symbol:
    :code:`r[i]`

Latex:
    :math:`{{\vec r}}_{i}`

Dimension:
    :code:`length`


.. py:data:: mass

    :attr:`~symplyphysics.symbols.basic.mass` of the :math:`i`-th body.

Symbol:
    :code:`m[i]`

Latex:
    :math:`{m}_{i}`

Dimension:
    :code:`mass`


.. py:data:: law

    :code:`r_com = Sum(m[i] * r[i], i) * Sum(m[i], i)^(-1)`


    ..
        For the Latex code printer:
        TODO: fix indexed vector symbols
        TODO: add parenthesis around IndexedSum when it is the base of an exponent

    Latex:
        .. math::
            {\vec r}_\text{COM} = \frac{\sum_i m_i {\vec r}_i}{\sum_i m_i}