... null space of constraint equations. In this paper, index-1 Lagrange’s equations are first considered, including the not-so-rare case of having a singular mass matrix and redundant constraints. The existence and uniqueness of solution for acceleration vector and Lagrange multipliers vector is studied...

... state vector and incomplete state vector availability. Using an equivalent algebraic description of dynamical systems by Chebyshev spectral collocation and data, a standard least-squares residual cost function is set up for complete and incomplete information cases. Minimization of this cost yields...

...Ahmed A. Shabana Slope discontinuities and T-sections can be modeled in a straight forward manner using fully parameterized absolute nodal coordinate formulation (ANCF) finite elements that have a complete set of gradient vectors. Linear transformations that define the element connectivity can...

... cannot be stored, and may not even be explicitly known. If it is known, the user has the option to provide the action of the Jacobian on a vector. An alternative strategy is also presented in which one may want to approximate the trajectory with a specialized solver, linearize around the computed...

..., the procedures are explained generally; then the technique to incorporate a fractional-order state vector into a conventional state equation is given as an example of the applications. The state-space representation in this study is useful not only to model a controlled system with fractional dynamics but also...