Quaternions in molecular modeling

Quaternions in molecular modeling.

Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational data, in the random sampling of rotations, and in establishing grids in orientation space. These examples show that many of the rotational problems that arise in...

NPSNET: Flight Simulation Dynamic Modeling Using Quaternions

The Naval Postgraduate School (NPS) has actively explored the design and implementation of networked, real time, three-dimensional battlefield simulations on low cost, commercially available graphics workstations. The most recent system, NPSNET, has improved in functionality to such an extent that it is considered a low cost version of the Defense Advanced Research Project Agency’s (DARPA) SIMN...

Exercises in Quaternions

Understanding quaternions

The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared for its importance with the invention of triple coordinates by Descartes. The ideas of this calculus, as distinguished from its operations and symbols, are fitted to be of the greatest use in all parts of science.-Clerk Maxwell, 1869. Quaternions came from Hamil...

Generalized Quaternions

The quaternion group Q8 is one of the two non-abelian groups of size 8 (up to isomorphism). The other one, D4, can be constructed as a semi-direct product: D4 ∼= Aff(Z/(4)) ∼= Z/(4) o (Z/(4))× ∼= Z/(4) o Z/(2), where the elements of Z/(2) act on Z/(4) as the identity and negation. While Q8 is not a semi-direct product, it can be constructed as the quotient group of a semi-direct product. We wil...