Newtonian Dynamics - Euclidean Structure

Euclidean Structure

The configuration space and the phase space of the dynamical system (3) both are Euclidean spaces, i. e. they are equipped with a Euclidean structure. The Euclidean structure of them is defined so that the kinetic energy of the single multidimensional particle with the unit mass is equal to the sum of kinetic energies of the three-dimensional particles with the masses :

T=\frac{\Vert\mathbf v\Vert^2}{2}=\sum^N_{i=1}m_i\,\frac{\Vert\mathbf v_i\Vert^2}{2}.

(4)

Read more about this topic:  Newtonian Dynamics

Famous quotes containing the word structure:

    “... the structure of a page of good prose is, analyzed logically, not something frozen but the vibrating of a bridge, which changes with every step one takes on it.”
    —Robert Musil (1880–1942)