Possible and Impossible (Momentum) Configurations

This chapter prepares a smooth way from Eulerian classical mechanics to quantum mechanics. Starting from Helmholtz’s foundation of the energy conservation law using Leibniz’s theorem as described in the foregoing Chapter 2, the configurations a system can (cannot) assume in a given stationary state are explored. The following constraints are taken into account: Newton-Euler’s exclusion principle, d’Alembertian constraints and constraints imposed by conservation laws. The set of possible and impossible momentum configurations is also considered, using Nemorarius’ theorem of the foregoing chapter.

Keywords: d’Alembertian constraints, Conservation laws, Helmholtz, Hodograph, Impossible configurations, Impossible momentum configurations, Leibniz’s theorem, Momentum configuration space, Nemorarius’ theorem, Newton-Euler’s exclusion principle, Possible configurations, Possible momentum configurations, Schütz, State, State function, Stationary state.