Editing Newtonian dynamics (section)

==Kinetic energy of a constrained Newtonian dynamical system==
Since the Euclidean structure of an unconstrained system of <math>\displaystyle N</math> particles is introduced through their kinetic energy, the induced Riemannian structure on the configuration space <math>\displaystyle N</math> of a constrained system preserves this relation to the kinetic energy:
{{NumBlk|:|<math>
T=\frac{1}{2}\sum^n_{i=1}\sum^n_{j=1}g_{ij}\,w^i\,w^j</math>.|{{EquationRef|12}}}}
The formula ({{EquationNote|12}}) is derived by substituting ({{EquationNote|8}}) into ({{EquationNote|4}}) and taking into account ({{EquationNote|11}}).