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| Content Provider | The American Society of Mechanical Engineers (ASME) Digital Collection |
|---|---|
| Author | Bru¨ls, Olivier Arnold, Martin Cardona, Alberto |
| Copyright Year | 2011 |
| Abstract | This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group. Those equations can then be solved using a Lie group time integration method proposed in a previous work. The general structure of the equations of motion are derived from Hamilton principle in a general and unifying framework. Then, in the case of rigid body dynamics, two particular formulations are developed and compared from the viewpoint of the structure of the equations of motion, of the accuracy of the numerical solution obtained by time integration, and of the computational cost of the iteration matrix involved in the Newton iterations at each time step. In the first formulation, the equations of motion are described on a Lie group defined as the Cartesian product of the group of translations R3 (the Euclidean space) and the group of rotations SO(3) (the special group of 3 by 3 proper orthogonal transformations). In the second formulation, the equations of motion are described on the group of Euclidean transformations SE(3) (the group of 4 by 4 homogeneous transformations). Both formulations lead to a second-order accurate numerical solution. For an academic example, we show that the formulation on SE(3) offers the advantage of an almost constant iteration matrix. |
| Sponsorship | Design Engineering Division and Computers and Information in Engineering Division |
| Starting Page | 85 |
| Ending Page | 94 |
| Page Count | 10 |
| File Format | |
| ISBN | 9780791854815 |
| DOI | 10.1115/DETC2011-48132 |
| Volume Number | Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B |
| Conference Proceedings | ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
| Language | English |
| Publisher Date | 2011-08-28 |
| Publisher Place | Washington, DC, USA |
| Access Restriction | Subscribed |
| Subject Keyword | Algebra Equations of motion Multibody systems Dynamics (mechanics) Rotation Kinematics |
| Content Type | Text |
| Resource Type | Article |
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