Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer...

A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this chapter. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down fini...

In this work, the quantized Hill problem is considered in order for us to study existence and stability of equilibrium points. particular, we have studied three different cases which give all whole possible locations two points are emerging from first case four second case, while third does not provide a realistic locations. Hence, obtained new related quantum perturbations. Furthermore, allowe...

Abstract Hydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they susceptible to oil whirl instability, may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical is investigate the stability bifurcations of system. Since closed form for finite forces not exist, nonlinear stiffness damping coefficients repr...

Abstract The quasi-bicircular problem (QBCP) is a periodic time-dependent perturbation of the Earth–Moon restricted three-body (RTBP) that accounts for effect Sun. It based on using solution Earth–Moon–Sun to write equations motion infinitesimal particle. paper focuses dynamics near $$L_1$$ L 1</mml:mn...

We present proofs of two classical theorems. The first one, due to Darboux and Sauer, states that infinitesimal rigidity is a projective invariant; the other one establishes relations (infinitesimal Pogorelov maps) between the infinitesimal motions of a Euclidean framework and of its hyperbolic and spherical images. The arguments use the static formulation of infinitesimal rigidity. The duality...