A list of open source physics engines

• Bullet, 3d, c++. (The same website for PyBullet)
  • AwayPhysics, an ActionScript 3 port of Bullet
  • Bullet-ANE, an Adobe Native Extension for Bullet
  • ammo.js, a port of the Bullet physics engine to JavaScript using Emscripten
  • Physijs, a physics plugin (based on ammo.js) for three.js
  • AmmoNext, a javascript port of the Bullet 3, based on ammo.js
  • Bullet.js, a JavaScript port of Bullet physics engine.
  • JBullet, a Java port of Bullet.
• ODE, 3d, c/c++ (c style APIs)
  • an active fork by unknown maintainers
  • a Go binding
• JoltPhysics, 3d, c++, A multi core friendly rigid body physics and collision detection library suitable for games and VR applications
• Bounce, 3d, c++
• nphysics, 2d and 3d, rust
• Rapier, another 2d and 3d physics engine in rust
• Bevy XPBD, a 2D and 3D physics engine based on Extended Position Based Dynamics (XPBD) for the Bevy game engine, in rust.
• Torque2D, 2d, c++
• Torque6, 2d, c++, loosely based on Torque2D
• Velocity Raptor, 2d, c
• Box2D, 2d, c++. (The lite version)
  • LiquidFun, a 2D rigid-body and fluid simulation C++ library based upon Box2D
  LiquidFun.js, a port of LiquidFun to JavaScript using using Emscripten
  • box2d.js. a JavaScript port of Box2D using Emscripten
  • Planck.js, another JavaScript port of Box2D, manually rewritten, not with Emscripten.
  • Box2DFlash. an ActionScript 3 port of Box2D 2.02 and 2.10
    • box2d-js is a JavaScript port of Box2D Physics Engine (converted from Box2DFlashA 1.4.3.1 in an automatic manner)
    • box2dweb is a JavaScript port of Box2D Physics Engine (converted from Box2DFlash 2.1a in an automatic manner)
  • wck (World Construction Kit ). a ActionScript 3 (using Alchemy) port of Box2D 2.10+
  • fbox2d, another ActionScript 3 port of Box2D 2.10+ revision 141.
  • pybox2d, a Python port of Box2D
  • JBox2D, a Java port of Box2D
  • Farseer, c#, based on Box2D
  • Box2D.go, a Go port of Box2D
  • go-box2d-lite, a Go port of Box2D-lite
• verlet, 2d, Go
• dyn4j, 2d, Java
• Jitter Physics - 3d, C#
• BEPUphysics v2 - 3d, C#, v1
• Jitter Physics - 3d, C#
• Cubez - 3d, C++
• Cubez - a Go port
• Nape, 2d, Haxe
• cannon.js, 3d, JavaScript
• Physijs (cannon branch), a physics plugin for three.js
• GoblinPhysics, 3d, JavaScript
• verlet-js, 2d, JavaScript, a simple verlet physics engine
• PhysicsJS, 2d, JavaScript
• Matter.js, 2d, JavaScript
• p2.js, 2d, JavaScript
• Coffee Physics, 2d, CoffeeScript (compiles into JavaScript.).
• JPE, 2d, JavaScript
• APE (Actionscript Physics Engine), 2d, ActionScript 3
• Chipmunk2D, 2d, c
• glaze, an ActionScript 3 port of Chipmunk2D
• Chipmunk-js, a port of the Chipmunk Physics library to Javascript
• a pure Go port
• a pure Go port
• a Go binding through cgo
• another Go binding through cgo
• Walaber's JelloPhysics, soft-body physics dynamics (not found its webpage)
• JelloAS3, an ActionScript port of JelloPhysics
• JelloHx, a Haxe port of JelloPhysics, based on JelloAS3
• Jello-Physics, a C# port of JelloPhysics
• JelloSwift, a Swift port of JelloPhysics
• Gravitle, 2D soft body engine, Rust
• JigLib, 3d, c++
  • JigLibflash, an ActionScript 3 port if JlgLib
  • JigLibJS2, a Javascript port of JlgLib, based on JiglibFlash
• Moby, 3d, c++, GPLv2
• Newton-Dynamics, 3d, c++
• OimoPhysics, 3d, ActionScript 3
• Oimo.js, a JavaScript port of OimoPhysics
• elm-physics, a highly experimental toy physics engine in Elm language.
• Traer Physics, a simple particle system physics engine for processing (language) and Java.
• qu3e, 3d, c++
• Tokamak, 3d, c++
• DynaMo, 3d, c++, GPL
• ReactPhysics3D, 3d, c++
• React, a Java port of ReactPhysics3D
• Chrono::Engine, 3d, c++
• PositionBasedDynamics, 3d, c++, a library for the physically-based simulation of rigid bodies, deformable solids and fluids.
• SPlisHSPlasH, 3d, c++, physically-based simulation of fluids
• MuJoCo Physics stands for Multi-Joint dynamics with Contact. It is a general purpose physics engine that aims to facilitate research and development in robotics, biomechanics, graphics and animation, machine learning, and other areas which demand fast and accurate simulation of articulated structures interacting with their environment. (to be open sourced)
• Rigs of Rods is a free/libre soft-body physics simulator mainly targeted at simulating vehicle physics. 3d, c++
• Physics3D, A 3D physics engine. c++

Here are some ones which may be not complete engines, but very good for study and education purposes:

• Experimenting with physics simulation
• myPhysicsLab
• Dyna-Kinematics

Along with these open sourced ones, there are some famous non-free (nor not universally free) ones:

• Nvidia's PhysX, which will perform much better if PPU (physics processing unit) is available for a graphics card. You can get the soure code (but not under an open source license) of PhysX by registering a Nivida developer account. (thank Morten Skaaning for the info) Update: PhysX has been open sourced now. See v4 and v5.
• More proprietary ones: Havok, Euphoria, DMM

Collision detection plays an important role in physics engine development. Here are some open source collision libraries:

• Awesome Collision Detection
• 18 Collision Detection Open Source Projects

In the end, some articles which are very helpful to physics engine development.

• Game physics from scratch, maintained by Liam
• Ten Minute Physics, maintained by Matthias Mueller

This list may be not complete. Welcome anybody to help me improve this list.