TY - JOUR AU - Tuan, Nguyen Thai Minh AU - Chung, Pham Thanh AU - Khoa, Do Dang AU - Phong, Phan Dang PY - 2019/02/18 Y2 - 2024/03/29 TI - Kinematic and dynamic analysis of multibody systems using the Kronecker product JF - Vietnam Journal of Science and Technology JA - Vietnam J. Sci. Technol. VL - 57 IS - 1 SE - Mechanical Engineering - Mechatronics DO - 10.15625/2525-2518/57/1/12285 UR - https://vjs.ac.vn/index.php/jst/article/view/12285 SP - 112-127 AB - <p>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.</p> ER -