World of (Rigid) Bodies Simulation Framework

World of Bodies (WoRB) is a framework for the real-time simulation of rigid bodies.

Documents

• Contacting Rigid Bodies
  Simulation of collisions between rigid bodies using the WoRB library. Validation of the simulation by studying the conservation of energy, linear momentum and angular momentum. Study of the simulation stability.
   
• Rigid Body Motion in 3D
  Theoretical framework. Mathematica notebook for a rigid body simulation using the Quat package. Notes on frames of reference are here.
   
• Rotations of Tensors using Quaternions
  An expression of spatial rotations of a (moment of inertia) tensor in the pure quaternionic form.
   
• Quat
  Mathematica package that implements Hamilton’s quaternion algebra. Allows symbolic transformations of quaternions to more extent than Mathematica's original.
   
• Quat Test Bed
  Regression tests for the Quat package.

How to use WoRB framework

Initialization

• Create a set of instances of Geometry and RigidBody
• Set mass and inertia tensor for the rigid bodies
• Set their initial location, orientation, velocity and angular velocity
• Apply any permanent external forces, e.g. gravity
• Create an instance of WorldOfRigidBodies
• Populate WorldOfRigidBodies::Objects with the list of instantiated rigid bodies

The main loop of the simulation

• Apply any temporary internal or external forces, e.g. spring forces or thrusts.
• Call WorldOfRigidBodies::SolveODE
• Render the bodies.

The single step of the simulation is in WorldOfRigidBodies::SolveODE, which performs the following steps

• Solve ODE on each body in the system
• Collision detection: find all collisions between all geometries
• Collision response: resolve all the collisions
• Update the internal derived quantities of the rigid bodies and geometries

Source Code

• C++ WoRB library and MATLAB source code

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Author:

Mikica B Kocic

Copyright:

GNU Public License.