On configurations of symbolic equations of motion for rigid multibody systems

1995 ◽  
Vol 30 (8) ◽  
pp. 1149-1170 ◽  
Author(s):  
Kan Cui ◽  
Imtiaz Haque ◽  
Mukundh Thirumalai
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Rigid Multibody Systems ◽  
Symbolic Equations Of Motion ◽  
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.

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

Constrained Multibody Dynamics With Python: From Symbolic Equation Generation to Publication

2013 ◽  
Author(s):  
Gilbert Gede ◽  
Dale L. Peterson ◽  
Angadh S. Nanjangud ◽  
Jason K. Moore ◽  
Mont Hubbard
Keyword(s):  
Open Source ◽  
Undergraduate Students ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Academic Research ◽  
General Purpose ◽  
Engineering Software ◽  
Symbolic Equations Of Motion ◽  
High Level

Symbolic equations of motion (EOMs) for multibody systems are desirable for simulation, stability analyses, control system design, and parameter studies. Despite this, the majority of engineering software designed to analyze multibody systems are numeric in nature (or present a purely numeric user interface). To our knowledge, none of the existing software packages are 1) fully symbolic, 2) open source, and 3) implemented in a popular, general, purpose high level programming language. In response, we extended SymPy (an existing computer algebra system implemented in Python) with functionality for derivation of symbolic EOMs for constrained multibody systems with many degrees of freedom. We present the design and implementation of the software and cover the basic usage and workflow for solving and analyzing problems. The intended audience is the academic research community, graduate and advanced undergraduate students, and those in industry analyzing multibody systems. We demonstrate the software by deriving the EOMs of a N-link pendulum, show its capabilities for LATEX output, and how it integrates with other Python scientific libraries — allowing for numerical simulation, publication quality plotting, animation, and online notebooks designed for sharing results. This software fills a unique role in dynamics and is attractive to academics and industry because of its BSD open source license which permits open source or commercial use of the code.

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