Constraint Reaction Forces and Lagrange Multipliers in Multi-Body Systems
The study performs the relation between the Lagrange multipliers and the constraint reaction forces in the multi-body systems. It helps to establish a simple and effective method to deal with the non-smooth factors including friction, contact and collision in multi-body systems. First, a general expression calculating the ideal constraint reaction forces is described by a form of complete Cartesian reference coordinate in a discrete dynamical system. Then, an explicit expression is given in the form of independent general generalized coordinates for a multi-body system. A condition under which the constraint reaction forces can be one-to-one corresponding to Lagrange multipliers is discussed. An example is used to demonstrate the process to realize the condition and the effectiveness of this method.
Zhengyi Jiang and Chunliang Zhang
W. L. Yao and Y. S. Ren, "Constraint Reaction Forces and Lagrange Multipliers in Multi-Body Systems", Advanced Materials Research, Vols. 97-101, pp. 2824-2827, 2010