Derivation of theories: structures of the derived system in terms of thoseof the original system in classical mechanics

We present the technique of derivation of a theory to obtain an (n + 1)f-de grees-of-freedom theory from an f-degrees-of-freedom theory and show that o ne can calculate all of the quantities of the derived theory from those of the original one. Specifically, we show that one can use this technique to construct, from an integrable system, other integrable systems with more de grees of freedom.