TY - JOUR
T1 - One kind motion of controllable constrained Birkhoffian system
T2 - the absence of constraints
AU - Chen, J.
AU - Mei, F. X.
AU - Liu, S. X.
AU - Guo, Y. X.
N1 - Publisher Copyright:
© 2020, The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - This paper is devoted to discuss the motion of controllable constrained Birkhoffian system along with its absence of constraints. The first step is to establish the autonomous and non-autonomous differential equations of motion of the system, based on Pfaff–Birkhoff principle. Secondly, the existence of constraint multipliers are exhaustively discussed. Thirdly, the definition of one kind motion of the system, called free motion, is given, which is described and analyzed by the absence of constraints that are determined by constraint multipliers. Lemma 2 illustrates that one system can realize its free motion by selecting proper control parameters. In particular, theorem 2 provides that one system can naturally realize free motion when we consider the integral of the unconstrained Birkhoffian system as the constraints of constrained Birkhoffian system. Finally, the results obtained are illustrated by several examples.
AB - This paper is devoted to discuss the motion of controllable constrained Birkhoffian system along with its absence of constraints. The first step is to establish the autonomous and non-autonomous differential equations of motion of the system, based on Pfaff–Birkhoff principle. Secondly, the existence of constraint multipliers are exhaustively discussed. Thirdly, the definition of one kind motion of the system, called free motion, is given, which is described and analyzed by the absence of constraints that are determined by constraint multipliers. Lemma 2 illustrates that one system can realize its free motion by selecting proper control parameters. In particular, theorem 2 provides that one system can naturally realize free motion when we consider the integral of the unconstrained Birkhoffian system as the constraints of constrained Birkhoffian system. Finally, the results obtained are illustrated by several examples.
KW - Absence of constraint
KW - Constrained Birkhoffian system
KW - Free motion
KW - Kinematic control
UR - https://www.scopus.com/pages/publications/85086114822
U2 - 10.1007/s10409-020-00961-4
DO - 10.1007/s10409-020-00961-4
M3 - Article
AN - SCOPUS:85086114822
SN - 0567-7718
VL - 36
SP - 735
EP - 741
JO - Acta Mechanica Sinica/Lixue Xuebao
JF - Acta Mechanica Sinica/Lixue Xuebao
IS - 3
ER -