Abstract We construct the exponential map associated to a nonholonomic system that allows us define an exact discrete constraint submanifold. reproduce continuous flow as on this submanifold deriving version of equations. Finally, we derive general family integrators includes particular case trajectory.

verything moves! In a world dominated by electronic devices and instruments it is easy to forget that all measurements involve motion, whether it be the motion of electrons through a transistor, Cooper pairs or quasiparti-cles through a superconducting quantum interference device (SQUID), photons through an optical interferome-ter—or the simple displacement of a mechanical element. Nanoscience ...

The theory of contact mechanics deals with stresses and deformations which arise when the surfaces of two solid bodies are brought into contact. In elastic deformation contact occurs over a finite area. A regular method for determining the dimensions of this area is Hertz Contact Model. Appearance of atomic force microscope results in introduction of Contact ...

T he story I want to tell you begins in March 1926 and ends in April 1926. Early in March two separate theories existed: matrix mechanics and wave mechanics. At the end of April these two had merged into one theory, more powerful than the two parents taken separately. Wave mechanics was based upon three fundamental hypotheses: A. Stationary states are determined by complexvalued wave functions ...

It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations.

In this paper using the Clifford algebra over R4 and its matrix representation, we construct Clifford scaling functions and Clifford wavelets. Then we compute related mask functions and filters, which arise in many applications such as quantum mechanics.