The acceleration form of constraint equations is utilized in this paper to solve for the inverse dynamics of servoconstraints. A condition for the existence of control forces that enforce servo-constraints is derived. For overactuated dynamical systems, the generalized Moore-Penrose inverse of the constraint matrix is used to parameterize the solutions for these control forces in terms of free ...

Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of adL. For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. The constructi...

A well–known property of an irreducible singular M–matrix is that it has a generalized inverse which is non–negative, but this is not always true for any generalized inverse. The authors have characterized when the Moore–Penrose inverse of a symmetric, singular, irreducible and tridiagonal M–matrix is itself an M–matrix. We aim here at giving new explicit examples of infinite families of matric...

Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of ad(L). For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. We apply our...

In this paper, we will study algebraic properties of the generalized inverses of the sum and the product of two matrices. By using rank additivity we explicit the generalized inverse of the sum of two matrices if their range spaces are not disjoint and we give a numerical example in this case. We will also use projectors to express the general form of a generalized inverse of the product of two...

In [8] Markov interval maps were introduced and it was shown that any two inverse limits with Markov interval bonding maps with the same pattern were homeomorphic. In this article we introduce generalized Markov interval functions, which are a generalization of Markov interval maps to set-valued functions, and show that any two generalized inverse limits with generalized Markov interval bonding...

Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X).) An operator S ∈ B(X) is a generalized inverse of T if TST = T . In this paper we look at several Banach algebras of operators and characterize when an operator in that algebra has a generalized inverse that is also in the algebra. Also, Drazin inverses will be related to generalized inverses and spectral pro...

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of Browder-Petryshyn type mapping. Our resultsimprove and extend the results announced by many others.