A comparative study of the principal methods for the analytical formulation and the numerical solution of the equations of motion of rigid multibody systems

2018 ◽  
Vol 88 (12) ◽  
pp. 2153-2177 ◽  
Author(s):  
Carmine Maria Pappalardo ◽  
Domenico Guida
Keyword(s):  
Comparative Study ◽  
Numerical Solution ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Analytical Formulation ◽  
Rigid Multibody Systems ◽  
Rigid Multibody

SYMBOLIC TREATMENT FOR THE EQUATIONS OF MOTION FOR RIGID MULTIBODY SYSTEMS

2010 ◽  
Vol 34 (1) ◽  
pp. 37-55 ◽  
Author(s):  
Bukoko C. Ikoki ◽  
Marc J. Richard ◽  
Mohamed Bouazara ◽  
Sélim Datoussaïd
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
The World ◽  
Rigid Multibody Systems ◽  
Symbolic Approach ◽  
Rigid Multibody

The library of symbolic C++ routines is broadly used throughout the world. In this article, we consider its application in the symbolic treatment of rigid multibody systems through a new software KINDA (KINematic & Dynamic Analysis). Besides the attraction which represents the symbolic approach and the effectiveness of this algorithm, the capacities of algebraical manipulations of symbolic routines are exploited to produce concise and legible differential equations of motion for reduced size mechanisms. These equations also constitute a powerful tool for the validation of symbolic generation algorithms other than by comparing results provided by numerical methods. The appeal in the software KINDA resides in the capability to generate the differential equations of motion from the choice of the multibody formalism adopted by the analyst.

scholarly journals Special Coordinates Associated With Recursive Forward Dynamics Algorithm for Open Loop Rigid Multibody Systems

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
Ashitava Ghosal
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Equations Of Motion ◽  
Special Property ◽  
Open Loop ◽  
Forward Dynamics ◽  
Rigid Multibody Systems ◽  
Two Stages ◽  
Rigid Multibody ◽  
General Tree

The recursive forward dynamics algorithm (RFDA) for a tree structured rigid multibody system has two stages. In the first stage, while going down the tree, certain equations are associated with each node. These equations are decoupled from the equations related to the node’s descendants. We refer them as the equations of RFDA of the node and the current paper derives them in a new way. In the new derivation, associated with each node, we recursively obtain the coordinates, which describe the system consisting of the node and all its descendants. The special property of these coordinates is that a portion of the equations of motion with respect to these coordinates is actually the equations of RFDA associated with the node. We first show the derivation for a two noded system and then extend to a general tree structure. Two examples are used to illustrate the derivation. While the derivation conclusively shows that equations of RFDA are part of equations of motion, it most importantly gives the associated coordinates and the left out portion of the equations of motion. These are significant insights into the RFDA.

Multiple impacts with friction in rigid multibody systems

1995 ◽  
Vol 7 (4) ◽  
pp. 471-497 ◽  
Author(s):  
Ch. Glocker ◽  
F. Pfeiffer
Keyword(s):  
Multibody Systems ◽  
Multiple Impacts ◽  
Rigid Multibody Systems ◽  
Rigid Multibody ◽  
Impacts With Friction

Rigid Multibody Systems: The Plastic Hinge Approach

2001 ◽  
pp. 205-237 ◽  
Author(s):  
J. A. C. Ambrósio ◽  
M. Seabra Pereira ◽  
J. F. A. Milho
Keyword(s):  
Multibody Systems ◽  
Plastic Hinge ◽  
Rigid Multibody Systems ◽  
Rigid Multibody
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