KINEMATIC AND DYNAMIC ANALYSIS OF MULTIBODY SYSTEMS USING THE KRONECKER PRODUCT

Authors

  • Nguyen Thai Minh Tuan
  • Chung Thanh Pham Trường Đại học Bách khoa Hà Nội
  • Do Dang Khoa
  • Phan Dang Phong

DOI:

https://doi.org/10.15625/2525-2518/57/1/12285

Keywords:

Jacobian matrix, Hessian matrix, Kronecker product, velocity-free Coriolis matrix, matrix form of Lagrange’s equations

Abstract

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.

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References

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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.

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Schiehlen W. and Eberhard P. - Applied Dynamics (Vol. 57), Springer, 2014, pp. 215.

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Published

2019-02-18

How to Cite

Tuan, N. T. M., Pham, C. T., Khoa, D. D., & Phong, P. D. (2019). KINEMATIC AND DYNAMIC ANALYSIS OF MULTIBODY SYSTEMS USING THE KRONECKER PRODUCT. Vietnam Journal of Science and Technology, 57(1), 112. https://doi.org/10.15625/2525-2518/57/1/12285

Issue

Section

Mechanical Engineering - Mechatronics