Editing Newtonian dynamics (section)

==Euclidean structure==
The configuration space and the phase space of the dynamical system ({{EquationNote|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 <math>\displaystyle m=1</math> is equal to the sum of kinetic energies of the three-dimensional particles with the masses <math>\displaystyle m_1,\,\ldots,\,m_N</math>:
{{NumBlk|:|<math>
T=\frac{\Vert\mathbf v\Vert^2}{2}=\sum^N_{i=1}m_i\,\frac{\Vert\mathbf v_i\Vert^2}{2}</math>.|{{EquationRef|4}}}}