Uslovi za dinamički balans krutog tela s teškim stopalom

Abstract

Opisan je model krutog tela i teškog stopala spojenih obrtnim zglobom u konstantnom gravitacionom polju. Kruto telo se kreće u vertikalnoj ravni, dok teško stopalo leži na ravnoj, vrlo hrapavoj horizontalnoj podlozi. Uslovi za dinamički balans ovog sistema matematički su izraženi koristeći metodu tačke nula momenta. Pokazuje se da oni određuju oblast u faznom prostoru u kojoj stanje sistema treba da bude da bi se dinamički balans sistema održao. Takođe se pogodnom simulacijom kretanja sistema u dinamičkom balansu pokazuje da ovi uslovi nisu dovoljni da sistem održi uspravan stav, već da su u vezi s njegovom upravljivošću. Ukratko se razmatra koji su neophodni uslovi da bi ovaj sistem u dinamičkom balansu zadržao uspravan stav.

The model of a rigid body and heavy foot joined by the revolute joint in the constant gravitational field is described. The rigid body moves in the vertical plane, whereas the heavy foot lies on the flat, very rough horizontal support. Conditions for the dynamic balance of this system are mathematically expressed by using the ZMP method. It is shown that they determine an area in the phase space in which the state of the system should be in order that its dynamic balance is kept. It is also shown by appropriate simulations of motion of the system in the dynamic balance that these conditions are not sufficient for the system to keep its upright posture, but are in connection with its controllability. It is briefly discussed what are the necessary conditions for this system in dynamic balance to keep its upright posture.