Abstract
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split quaternions.
Highlights
Quaternions and dual quaternions provide compact and simple parametrizations for the groups SO(3), SE(2) and SE(3)
Factorization of polynomials corresponds to the decomposition of a rational motion into rational motions of lower degree
The theory of quaternion polynomial factorization [4,13] has been extended to the dual quaternion case and numerous applications have been found [9,10,11]
Summary
Quaternions and dual quaternions provide compact and simple parametrizations for the groups SO(3), SE(2) and SE(3). This accounts for their importance in fields such as kinematics, robotics and mechanism science. In this context, polynomials over quaternion rings in one indeterminate can be used to parameterize rational motions. The theory of quaternion polynomial factorization [4,13] has been extended to the dual quaternion case and numerous applications have been found [9,10,11]. As of today our general understanding of dual quaternion factorization is quite profound but some
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