Automated independent coordinates' switching for the solution of stiff DAEs with the linearly implicit Euler method
The real time (RT) integration of the equations of motion describing complex mechanical systems requires the employment of proper integration schemes which must be able to handle the time integration at each time step in less than an a priori fixed sampling time interval. The linearly implicit Euler method has been successfully employed for the RT integration of large stiff differential algebraic systems of equations (DAEs) which typically arise from the complex mechanical systems of interest in practical applications. The current industry demand is to further increase the degree of complexity of multibody models employed in RT applications, pushing researchers to improve the efficiency of the currently available integration methods. In this paper, we investigate the improvements in the efficiency of the linearly implicit Euler method coming from the conversion of the equations of motion at each time step from a dependent to an independent coordinates' formulation. The automatic switching from dependent to independent coordinates is achieved exploiting the properties of the matrix R whose columns represent a basis of the null space of the constraint Jacobian matrix. A non iterative projection method is also applied in order to avoid the drift off from the constraint conditions.