Kinematic and dynamic analysis of multibody systems using the Kronecker product
Author affiliations
DOI:
https://doi.org/10.15625/2525-2518/57/1/12285Abstract
This paper employ Khang’s definition of the partial derivative of a matrix with respect to a vector and the Kronecker product to define translational and rotational Hessian matrices. With these definitions, the generalized velocities in the expression of a linear acceleration or an angular acceleration are collected into a quadratic term. The relations of Jacobian and Hessian matrices in relative motion are then established. A new matrix form of Lagrange’s equations showing clearly the quadratic term of generalized velocities is also introduced.
Downloads
References
Zhao Tieshi, et al. - Kinematics and Dynamics Hessian Matrices of Manipulators Based on Screw Theory, Chin. J. Mech. Eng., 28 (2015) 226-235.
Wen-Hua D., et al. - Control-orientated dynamic modeling of forging manipulators with multi-closed kinematic chains, Robotics and Computer-Integrated Manufacturing, 30 (5) (2014) 421-431.
Nguyen Van Khang - Consistent definition of partial derivatives of matrix functions in dynamics of mechanical systems, Mechanism and Machine Theory, 45 (2010) 981-988.
Nguyen Van Khang - Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems, Mechanics Research Communications, 38 (2011) 294-299.
Fuzhen Z. - Matrix Theory: Basic Results and Techniques, Springer New York, 2011, pp. 399.
Brewer J. - Kronecker products and matrix calculus in system theory, IEEE Transactions on Circuits and Systems, 25 (9) (1978) 772-781.
Laub A.J. - Matrix Analysis for Scientists and Engineers, SIAM, 2005, pp. 157.
Nguyen Van Khang - Dynamics of Multibody Systems, (second printing with some corrections and additions) (in Vietnamese). Hanoi Science and Technics Publishing House, 2017.
Schiehlen W. and Eberhard P. - Applied Dynamics (Vol. 57), Springer, 2014, pp. 215.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Vietnam Journal of Sciences and Technology (VJST) is an open access and peer-reviewed journal. All academic publications could be made free to read and downloaded for everyone. In addition, articles are published under term of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA) Licence which permits use, distribution and reproduction in any medium, provided the original work is properly cited & ShareAlike terms followed.
Copyright on any research article published in VJST is retained by the respective author(s), without restrictions. Authors grant VAST Journals System a license to publish the article and identify itself as the original publisher. Upon author(s) by giving permission to VJST either via VJST journal portal or other channel to publish their research work in VJST agrees to all the terms and conditions of https://creativecommons.org/licenses/by-sa/4.0/ License and terms & condition set by VJST.
Authors have the responsibility of to secure all necessary copyright permissions for the use of 3rd-party materials in their manuscript.
Vietnam Journal of Science and Technology (VJST) is pleased to notice: