Some Properties of Second Order Dynamic Systems with Parametric Resonances

1981 ◽  
pp. 71-75
Author(s):  
I. Gumowski
Keyword(s):  
Dynamic Systems ◽  
Second Order ◽  
Parametric Resonances

Consensus of second-order multi-agent dynamic systems with quantized data

2012 ◽  
Vol 376 (4) ◽  
pp. 387-393 ◽  
Author(s):  
Zhi-Hong Guan ◽  
Cheng Meng ◽  
Rui-Quan Liao ◽  
Ding-Xue Zhang
Keyword(s):  
Dynamic Systems ◽  
Second Order ◽  
Multi Agent

DYNAMIC SYSTEMS OF THE SECOND ORDER

1966 ◽  
pp. 253-350
Author(s):  
A.A. ANDRONOV ◽  
A.A. VITT ◽  
S.E. KHAIKIN
Keyword(s):  
Dynamic Systems ◽  
Second Order

On the Use of Lie Group Time Integrators in Multibody Dynamics

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Olivier Brüls ◽  
Alberto Cardona
Keyword(s):  
Lie Group ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Second Order ◽  
Order Accuracy ◽  
Time Integrators ◽  
Group Time ◽  
Constrained Equations ◽  
New Algorithms

This paper proposes a family of Lie group time integrators for the simulation of flexible multibody systems. The method provides an elegant solution to the rotation parametrization problem. As an extension of the classical generalized-α method for dynamic systems, it can deal with constrained equations of motion. Second-order accuracy is demonstrated in the unconstrained case. The performance is illustrated on several critical benchmarks of rigid body systems with high rotation speeds, and second-order accuracy is evidenced in all of them, even for constrained cases. The remarkable simplicity of the new algorithms opens some interesting perspectives for real-time applications, model-based control, and optimization of multibody systems.

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