Gepeszmernoki feladatok megoldasakor, ahol mozgasok leirasa, tervezese a cel, hagyomanyosan folytonos szemlelet dominal. A műszaki-technologiai fejlesztes azonban sok olyan rezgesi problemaba utkozott az utobbi evtizedben, ahol a fejlődes tovabbi korlatjat jelentő rezgeseket diszkret hatasok okozzak. Ennek alappeldai a robotika rezgesi jelensegei, ahol a newtoni dinamikaval leirhato, folytonosan viselkedő rendszert mikroprocesszorok segitsegevel szabalyoznak, es igy a mintavetelezesen es kerekitesi hibakon keresztul időbeli es terbeli digitalis hatasokat kapcsolnak hozza. Diszkret es folytonos rendszerek dinamikajanak egyuttes vizsgalatara szukseg van akkor is, ha a fizikai rendszer maga szabalyozza a folytonos rendszert diszkret modon, mint a nagy amplitudoju szerszamgeprezgesek, a gyorsan forgo tengelyek rubbing jelensege, vagy a kerekek terbeli gordulese es csuszasa soran jelentkező kapcsolgatas eseten. Olyan algoritmusokat dolgoztunk ki, amelyek a lehető legkevesebb numerikus kozelitest tartalmazva, pontosan es egyszerűen adjak meg az ilyen rendszerek stabilitasanak felteteleit, illetve a stabilitasveszteskor kialakulo rezgesek jelleget, frekvenciait, amplitudoit. Ezekkel a modszerekkel sikerult pl. robotok emberekkel valo erintkezesehez szukseges erőszabalyozasokat terveznunk az EU rehabilitacios robot projektjeben, uj nagysebessegű marasi technologiakat javasolnunk, magyarazatot adnunk kerekek fekezeskor kialakulo lateralis (simmiző) rezgesere. | Time-continuous approach dominates the solution of those problems of mechanical engineering where the goal is the analysis or design of certain motions. The technological development, however, has often been set back during the last decade by vibration problems originated in discrete effects. Basic example is the vibration phenomenon of robots, where the continuous physical system described the Newtonian laws is subjected to control by means of microprocessors. These introduce digital effects both in time and space via the sampling and the round-off, respectively. The coupled discrete and continuous systems dynamics are in the focus of critical vibration phenomena also in those cases when the physical system regulates itself in a discrete way. This happens during the large amplitude oscillations of machine tools, the rubbing phenomenon of rotors, or the subsequent switches between the rolling and sliding dynamics of wheels. We developed algorithms that give the stability conditions of these systems in a reliable, efficient and still simple way. Moreover, these methods also describe the nature of these vibrations, provide their frequency content and amplitude range. This way, for example, we designed the force control of rehabilitation robots in an EU project where human and robot must interact by touching each other, suggested new technological parameter domains for high-speed milling, or explained the lateral vibrations (shimmy) of wheels during braking.