Non-holonomic Constraint Force Postulates

The extended Hamilton's Principle and other methods proposed to handle non-holonomic constraints are considered. They dont agree with each other. By looking at its consistency with D'Alembert's principle for linear non-holonomic constraints, it was claimed in earlier papers that the direct extension of hamilton's principle is incorrect. Nonholonomic Constraints, linear in velocities were considered for this purpose. This paper analyses these claims, and shows that they are incorrect. And hence it shows that it is theoretically impossible to judge any attempt on non-holonomic constraints to be wrong, as long as they are consistent with the D'Alembertian for holonomic constraints.