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A method for calculating trajectories independent of the explicit determination of an object's equation of motion

Vyatkin Sergey, Korobeinikova Tetiana, Mykhaylov Pavlo, Chekhmestruk Roman, Vodzinska Oksana, Ovcharuk Vasyl, Kotyra Andrzej, Kashaganova Gulzhan, Julayeva Zhazira

Przegląd Elektrotechniczny

2021

R. 97, nr 9

34--37

A method for calculating the trajectory of a physical object that does not rely on explicitly setting the equation of motion is proposed. We analyze the problems and formulate requirements for the developed model. The choice of the motion algorithm is justified. The paper describes the technical part of the developed model and the logical structure of the program. The application contains the results of testing the system.

Zaproponowano metodę obliczania trajektorii obiektu fizycznego, która nie polega na jawnym wyznaczaniu równania ruchu. Przeanalizowano problemy i sformułowano wymagania dla opracowanego modelu. Uzasadniony jest wybór algorytmu ruchu. W pracy opisano część techniczną opracowanego modelu oraz strukturę logiczną programu. Aplikacja zawiera wyniki testowania systemu.

Euler-Poincare reduction of externally forced rigid body motion

Wiśniewski R., Kulczycki P.

Control and Cybernetics

2004

Vol. 33, no 2

297-310

If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincare reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modeling, estimation and control of mechanical systems. A control system generates an external force, which may break the symmetry in the dynamics. This paper shows how to model and to control a mechanical system on the reduced phase space, such that complete state space asymptotic stabilization can be achieved. The paper comprises a specialization of the well-known Euler-Poincare reduction to a rigid body motion with forcing. An example of satellite attitude control illustrates usefulness of the Euler-Poincare reduction in control engineering. This work demonstrates how the energy shaping method applies for Euler-Poincare equations.