In this paper, we introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms are partially linear which results from a well-known fact that un-deractuated systems can be partially linearized using a change of control 12]. The diiculty arises when the new control appears both in the linear and nonlin-ear subsystems. We introduce...

We consider differentiable dynamical systems generated by a diffeomorphism or a vector field on a manifold. We restrict to the finite-dimensional case, although some of the ideas can also be developed in the general case [21]. We also restrict to the behavior near a stationary point or a periodic orbit of a flow. Let the origin 0 of R be a stationary point of a C vector field X, i.e. X(0) = 0. ...

We introduce in this paper normal twistor equations for differential forms and study their solutions, the so-called normal conformal Killing forms. The twistor equations arise naturally from the canonical normal Cartan connection of conformal geometry. Reductions of its holonomy are related to solutions of the normal twistor equations. The case of decomposable normal conformal holonomy represen...

In this paper we present a framework for the combination of modal and temporal logic. This framework allows us to combine diier-ent normal forms, in particular, a separated normal form for temporal logic and a rst-order clausal form for modal logics. The calculus of the framework consists of temporal resolution rules and standard rst-order resolution rules. We show that the calculus provides a ...

We mean by a normal form a finite set of ordered pairs of subsets of a fixed set that fulfils two conditions: elements of it consist of disjoint sets and elements of it are incomparable w.r.t. inclusion. The underlying set corresponds to a set of propositional variables but is arbitrary. The correspodents to a normal form of a formula, e.g. a disjunctive normal form, is as follows. The normal f...