Embody

Embody is an F# library that allows you to easily define, execute, and validate $n$-body simulations.

Summary

Embody started out as an interactive .NET notebook where you could simulate and evaluate $n$-body systems (most notably, the Earth-Moon-Sun system, and Jupiter with its myriad of moons). The notebook kept on growing, so ultimately most of the code was moved into a separate package.

Currently, Embody is a single package that tackles a couple different responsibilities, including: vector operations, numerical integration, and plot visualisation.

Getting started

The standard way of working with the library is via interactive .NET notebooks.

Prerequisites

• VS Code
• .NET 6 SDK
• .NET Interactive Notebooks extension

First notebook

In order to create a blank notebook:

1. Press Ctrl + Shift + P in VS Code editor.

2. Select the ".NET Interactive: Create new blank notebook" option.

3. Select "Create as .dib".

4. Select "F#".

5. The notebook should open. Type the following line into the code block:

   #r "nuget: Embody"

   and then press Shift + Enter or press "Execute cell".

   In general, you should specify a package version after the package name, like this: #r "nuget: Embody, 0.2.0". For the most recent version, please check the "Script & Interactive" tab at the Package page.

6. After the package is imported, you can perform a simple vector arithmetic to verify if the package works. Type the following code into the second code block:

   open Embody.LinearAlgebra
   
   let a = vector3 0.1 0.2 0.3
   let b = vector3 1.0 2.0 3.0
   
   a + b

   After executing the cell, you should see the following output:

   x	y	z
   1.1	2.2	3.3

7. Congratulations! You've successfully created a .NET interactive notebook, and imported the Embody package. The next step would be to define an $n$-body system. Example(s) can be found here.

Future plans / TODOs

• Documentation page.
• Theoretical background behind implemented numerical methods and orbital simulations.
• Performance optimization.
• Memory usage consideration (it is currently a bit too easy to have all your RAM consumed by a long-running simulation).