Anholonomic Transformations of Mechanical Action Principle

We exhibit the transformation properties of the mechanical action principle under anholonomic transformations. Using the fact that spaces with torsion can be produced by anholonomic transformations we derive the correct action principle in these spaces which is quite different from the conventional action principle. ∗Work supported by the Commission of the European Communities in Science and Technology, Contract No. ERB3510PL920264, by the Sofia University Foundation for Scientific Reaserches, Contract No.3052-230/94, and by the International Atomic Energy Agency, UNESCO and International Centre for Theoretical Physics, Trieste, Italy.