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- CUBIC SPLINES IN THE GRASSMANN MANIFOLD GENERATED BY THE DE CASTELJAU ALGORITHMPublication . Pina, FátimaWe present a detailed analysis of the De Casteljau algorithm to gen erate cubic polynomials satisfying certain boundary conditions in the Grassmann manifold, and extend this approach to produce cubic splines that also solve inter polation problems on that manifold.
- COMPLETE CONTROLLABILITY OF THE KINEMATIC EQUATIONS DESCRIBING PURE ROLLING OF GRASSMANNIANSPublication . Pina, FátimaThis paper studies the controllability properties of certain nonholo nomic control systems, describing the rolling motion of Grassmann manifolds over the affine tangent space at a point. The control functions correspond to the freedom of choosing the rolling curve. The nonholonomic constraints are imposed by the non-slip and non-twist conditions on the rolling. These systems are proved to be controllable in some submanifold of the group of isometries of the space where the two rolling manifolds are embedded. The constructive proof of controllability is also partially addressed.
- COMPLETE CONTROLLABILITY OF THE KINEMATIC EQUATIONS DESCRIBING PURE ROLLING OF GRASSMANNIANSPublication . Pina, FátimaThis paper studies the controllability properties of certain nonholo nomic control systems, describing the rolling motion of Grassmann manifolds over the affine tangent space at a point. The control functions correspond to the free dom of choosing the rolling curve. The nonholonomic constraints are imposed by the non-slip and non-twist conditions on the rolling. These systems are proved to be controllable in some submanifold of the group of isometries of the space where the two rolling manifolds are embedded. The constructive proof of controllability is also partially addressed.
- Controllability of the kinematic equations describing pure rolling of GrassmanniansPublication . Pina, FátimaThis paper studies the controllability properties of certain nonholonomic control systems, describing the rolling motion of Grassmann manifolds over the affine tangent space at a point. The control functions correspond to the freedom of choosing the rolling curve. The nonholonomic constraints are imposed by the no-slip and no-twist conditions on the rolling. These systems are proved to be controllable in some submanifold of the group of isometries of the space where the two rolling manifolds are embedded. The constructive proof of controllability is also addressed
- CUBIC SPLINES IN THE GRASSMANN MANIFOLD GENERATED BY THE DE CASTELJAU ALGORITHMPublication . Pina, FátimaWe present a detailed analysis of the De Casteljau algorithm to gen erate cubic polynomials satisfying certain boundary conditions in the Grassmann manifold, and extend this approach to produce cubic splines that also solve inter polation problems on that manifold.