The mass spectrum of high energy elementary particles via El Naschie’s golden mean nested oscillators, the Dunkerly–Southwell eigenvalue theorems and KAM

In the present work we give a classical nested mechanical model and corresponding expressions for the theoretical masses of elementary particles, including the masses of quarks as being the joint eigenvalues of combined vibrating sets using the Southwell and the Dunkerly theorems. The role played by the golden mean in KAM theory and consequently our present model is also discussed.