Functions of matrices have been studied for as long as matrix algebra itself. Indeed, in his
seminal A Memoir on the Theory of Matrices (1858), Cayley investigated the square root of a …

In this paper, we study the use of the Chebyshev semi-iterative approach in projective and
position-based dynamics. Although projective dynamics is fundamentally nonlinear, its …

We consider the two logarithmic strain measures=||\mathrm dev _n\mathrm log U||=||\mathrm
dev _n\mathrm log F^ TF||\quad and\quad\vol=|\mathrm tr (\mathrm log U)=|\mathrm tr …

The possibility to introduce a new relative rotation tensor in the field of nonlinear micropolar
continua is discussed in the present paper. The proposed deformation tensor is able to …

In this paper we rediscover Grioli's important work on the optimality of the orthogonal factor
in the polar decomposition in an euclidean distance framework. We also draw attention to …

We propose rotation inferred from the polar decomposition of the flow gradient as a
diagnostic for elliptic (or vortex-type) invariant regions in non-autonomous dynamical …

Interpolation of motion is required in various fields of engineering such as computer
animation and vision, trajectory planning for robotics, optimal control of dynamical systems …

The unitary polar factor Q=U_p in the polar decomposition of Z=U_p\,H is the minimizer over
unitary matrices Q for both ‖\rmLog(Q^*Z)‖^2 and its Hermitian part ‖\rmsym__*\!(\rmLog …

We propose an algorithm for computing the polar decomposition of a 3× 3 real matrix that is
based on the connection between orthogonal matrices and quaternions. An important …

A nonlinear small-strain elastic theory is constructed from a systematic expansion in Biot
strains, truncated at quadratic order. The primary motivation is the desire for a clean …