Editing Newtonian dynamics (section)

==Embedding and the induced Riemannian metric==
Geometrically, the vector-function ({{EquationNote|7}}) implements an embedding of the configuration space <math>\displaystyle M</math> of the constrained Newtonian dynamical system into the <math>\displaystyle 3\,N</math>-dimensional flat configuration space of the unconstrained 
Newtonian dynamical system ({{EquationNote|3}}). Due to this embedding the Euclidean structure of the ambient space induces the Riemannian metric onto the manifold <math>\displaystyle M</math>. The components of the [[metric tensor]] of this induced metric are given by the formula
{{NumBlk|:|<math>\displaystyle g_{ij}=\left(\frac{\partial\mathbf r}{\partial q^i},\frac{\partial\mathbf r}{\partial q^j}\right)
</math>,|{{EquationRef|11}}}}
where <math>\displaystyle(\ ,\ )</math> is the scalar product associated with the Euclidean structure ({{EquationNote|4}}).