Embedding and The Induced Riemannian Metric
Geometrically, the vector-function (7) implements an embedding of the comfiguration space of the constrained Newtonian dynamical system into the -dimensional flat comfiguration space of the unconstrained Newtonian dynamical system (3). Due to this embedding the Euclidean structure of the ambient space induces the Riemannian metric onto the manifold . The components of the metric tensor of this induced metric are given by the formula
-
,
(11)
where is the scalar product associated with the Euclidean structure (4).
Read more about this topic: Newtonian Dynamics
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