Linearizing the equations of motion for multibody systems using an orthogonal complement method

The equations of motion of a multibody system are linearized and reduced to independent coordinates, using an orthogonal complement method. The orthogonal complement is used to eliminate the terms that result from a variation of the constraint forces. The resulting equations contain the derivative of the constraint Jacobian with respect to the coordinate vector in the stiffness matrix. The technique is suitable for a computer implementation. Examples are used to illustrate the process.