This chapter deals with the all-important notion of state as it is central to
all parts of physics. For this book, most important are, on the one hand, the notions
of state by Newton and Euler – on the other hand, the notion of state by Lagrange
and Laplace used nowadays. Surprisingly enough, Newton and Euler’s notions of
state are closer to quantum mechanics than the nowadays’ one. Newton’s axiomatic
contains solely the conservation of states (1st and 3rd axioms) and the change of
states (2nd axiom). In contrast, the equation of motion is not part of the axiomatic.
Euler’s axiomatic contains solely the conservation of states. The change of state
(and subsequently the equation of motion) is to be examined according to the
problem under consideration. In contrast to Newton’s axiomatic and correcting
Bohr’s corresponding claim, Euler’s principles of state change for classical bodies
are formulated such, that they can be translated even to quantum-mechanical
motion. Their power is also demonstrated through an alternative derivation of
Hamilton’s equation of motion.
Keywords: d’Alembert’s principle, Axiomatic, Dynamics, Euler’s principles of
stationary-state change, Hamiltonian, Inertia, Newton’s axioms, State, State
function, Statics, Stationary state.
