Kinematic and dynamic analysis of multibody systems using the Kronecker product - Tuan, Nguyen Thai Minh; Chung, Pham Thanh; Khoa, Do Dang; Phong, Phan Dang (Vietnam Journal of Science and Technology, 2019)
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.