Störmer-Verlet Integration Scheme for Multibody System Dynamics in Lie-Group Setting

Störmer-Verlet integration scheme has many attractive properties when dealing with ODE systems in linear spaces: it is explicit, 2nd order, linear/angular momentum preserving and it is symplectic for Hamiltonian systems. In this paper we investigate its application for numerical simulation of the multibody system dynamics (MBS) by formulating Störmer-Verlet algorithm for the rotational rigid body motion in Lie-group setting. Starting from the investigations on the single free rigid body rotational dynamics, the paper introduces modified RATTLE integration scheme with the direct SO(3) rotational update. Furthermore, non-canonical Lie-group Störmer-Verlet integration scheme is presented through the different derivation stages. Several presented numerical examples show excellent conservation properties of the proposed geometric algorithm.

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The constraint-stabilized implicit methods on Lie group for differential-algebraic equations of multibody system dynamics

Advances in Mechanical Engineering ◽

10.1177/1687814019842406 ◽

2019 ◽

Vol 11 (4) ◽

pp. 168781401984240

Author(s):

Jieyu Ding ◽

Zhenkuan Pan ◽

Wei Zhang

Keyword(s):

System Dynamics ◽

Lie Group ◽

Multibody System ◽

Differential Algebraic Equations ◽

Multibody System Dynamics ◽

Algebraic Equations ◽

Implicit Methods

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Advances in Transfer Matrix Method of Multibody System

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C ◽

10.1115/detc2009-86433 ◽

2009 ◽

Cited By ~ 1

Author(s):

Xiaoting Rui ◽

Guoping Wang ◽

Laifeng Yun ◽

Bin He ◽

Fufeng Yang ◽

...

Keyword(s):

System Dynamics ◽

Transfer Matrix ◽

Transfer Matrix Method ◽

Matrix Method ◽

Multibody Systems ◽

Multibody System ◽

Engineering Problem ◽

Multibody System Dynamics ◽

Integration Scheme ◽

Linear And Nonlinear

Multibody system dynamics has become important theoretical tool for wide engineering problems analysis in the world. Transfer matrix method of multibody system (MS-TMM) is a new approach for multibody system dynamics, which is developed in 20 years. In this paper, the transfer matrix method for linear and nonlinear multibody systems are introduced respectively. For linear multibody systems, the new concept of body dynamics equation and augmented eigenvector, the construction method of orthogonality, and the computing method of vibration characteristics and dynamic response are introduced; For nonlinear multibody systems, the discrete time transfer matrix method of multibody system (MS-DT-TMM) are presented. The apply of the transfer matrix method for multibody systems with tree, closed loop and network structures are also introduced. The transfer matrix method has good characteristics: 1 It does not require overall dynamics equations of system and simplify the solution procedure. 2 It has high computing speed, because the system matrices are always small irrespective of the size of a system. 3 It avoids the difficulties caused by developing overall dynamic equations of a system and by computing too high order matrices. 4 It provides maximum flexibility in modeling various configurations of multibody systems, by creating library of transfer matrices and assembling them easily, and by introducing any suitable numerical integration scheme. The new method is efficient for linear and nonlinear multi-rigid-flexible-body system, and it has been paid great attention, because many engineering problem of important mechanical system were solved effectively by using this method.

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