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:

    “When a house is tottering to its fall,
    The strain lies heaviest on the weakest part,
    One tiny crack throughout the structure spreads,
    And its own weight soon brings it toppling down.”
    —Ovid (Publius Ovidius Naso)