Hamilton Mechanics

Abstract

This chapter goes in for a further development of the theory of Classical Mechanics The main goal is thereby not so much the evolution and presentation of new auxiliary calculation tools. Furthermore, we will see that the Hamiltonian version of Classical Mechanics does not provide any new physics. Its range of validity and application corresponds namely rather exactly to that of the Lagrangian version. What it is about is rather to gain a deeper insight into the formal mathematical structure of the physical theory, and to investigate all thinkable reformulations of the basic principles. Aside from that we have to bear in mind that Classical Mechanics as any other physical theories possesses only a restricted range of validity which is not ‘a priori’ clear, however, the representation will turn out to be especially convenient for subsequent generalizations. Concept formations and mathematical correlations of the Hamiltonian formalism will prove to be helpful for a connection to the principles of the superordinate Quantum Mechanics. In the last analysis, that is the decisive motivation to deal with the Hamiltonian version of Classical Mechanics.