Python Calculate Center of Mass of N D Points

Introduction

The center of mass (COM) is a crucial concept in physics and engineering that represents the average position of all the mass in a system. For a set of discrete points, the center of mass can be calculated using their positions and masses.

This calculator helps you compute the center of mass for N points in D dimensions using Python. The implementation uses NumPy for efficient array operations, making it suitable for both small and large datasets.

Center of Mass Formula

The center of mass for a set of N points in D dimensions is calculated using the following formula:

This formula calculates the weighted average of all point coordinates, where the weights are the masses of the points.

Python Implementation

Here's a Python function that calculates the center of mass for N points in D dimensions using NumPy:

import numpy as np

def calculate_center_of_mass(points, masses):
    """
    Calculate the center of mass for N points in D dimensions.

    Parameters:
    points (numpy.ndarray): Array of shape (N, D) containing point coordinates
    masses (numpy.ndarray): Array of shape (N,) containing point masses

    Returns:
    numpy.ndarray: Center of mass coordinates of shape (D,)
    """
    total_mass = np.sum(masses)
    weighted_sum = np.sum(points * masses[:, np.newaxis], axis=0)
    center_of_mass = weighted_sum / total_mass
    return center_of_mass

The function takes two NumPy arrays as input: one containing the point coordinates and another containing the masses. It returns the center of mass coordinates as a NumPy array.

Worked Example

Let's calculate the center of mass for three points in 2D space with the following coordinates and masses:

Using the formula:

The center of mass is at coordinates (3.6, 4.6).