Dynamic equations of motion for mechanical systems with regard to Lagrange’s equation of motion are discussed. The case of redundant constraints and positive semidefinite mass matrix in obtaining the Lagrangian multipliers and the constraint forces corresponding to a constraint equation based on a generalized inverse of a rectangular matrix and Singular Value Decomposition (SV D) is detailed. Different ways of applying the generalized inverse of a matrix in relation to obtaining an acceleration of a mechanical system on which a holonomic constraint is imposed is investigated. It is established that there could be an infinite set of solutions for an acceleration and Lagrangian multipliers of a dynamic system. The conditions that need to be satisfied for an equation of a mechanical system to have a unique solution is also spelled out and ascertained by proof. Method of obtaining the generalized inverse of a matrix is also discussed. A numerical example is given to show the application of the methods.
Generalized Inverse, Holonomic Constraint, Positive definite matrix, Positive Semidefinite matrix, Rank Deficient Matrix, Redundant Constraints, Singular Mass matrix, Singular Value Decomposition, Обобщенная обратная матрица, голономная связь, положительно определённая матрица, знакопостоянная положительная матрица, ранг матрицы, избыточная связь, сингулярная матрица, разложение по сингулярным числам матрицы
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