Rigid Body Dynamics and Conformal Geometric Algebra

  • Anthony Lasenby
  • Robert Lasenby
  • Chris Doran


We discuss a fully covariant Lagrangian-based description of 3D rigid body motion, employing spinors in 5D conformal space. The use of this space enables the translational and rotational degrees of freedom of the body to be expressed via a unified rotor structure, and the equations of motion in terms of a generalised ‘moment of inertia tensor’ are given. The development includes the effects of external forces and torques on the body. To illustrate its practical applications, we give a brief overview of a prototype multi-rigid-body physics engine implemented using 5D conformal objects as the variables.


Rigid Body Rigid Body Motion Body Frame Inertia Tensor Rigid Body Dynamic 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Cavendish Laboratory and Kavli Institute for CosmologyUniversity of CambridgeCambridgeUK
  2. 2.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK
  3. 3.Sidney Sussex CollegeUniversity of Cambridge and Geomerics Ltd.CambridgeUK

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