Abstract
The partial derivatives of scalar functions, vector functions, and matrix functions with respect to a vector variable have many practical applications in the study of dynamics and control of mechanical systems . The paper firstly presents an overview of the matrix calculus related to Kronecker products . Secondly, two theorems establishing the relationship between the time derivative of a matrix and its partial derivative with respect to a vector, and the partial derivative of the product of two matrices with respect to a vector will be presented. Finally, a new matrix form of Lagrangian equations is developed to demonstrate the usefulness of these theorems in the study of dynamics of mechanical systems.
Published Version
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