Second-order constraints for equations of motion of constrained systems

Motivated by the Udwadia and Kalaba equation, it is suggested that one can take the advantage of the second-order form of constraint in a more global sense. The second-order form is especially useful in deriving equations of motion that are uncoupled and Lagrangian multiplier free. As a demonstration, the procedure of incorporating the second-order form into the Maggi's equation and Lagrange's equation is outlined. We consider both holonomic and nonholonomic cases.