Modeling and simplification for dynamic systems with testing procedures and metric decomposition

The author discusses a general simplification method for arbitrary dynamic systems which follow the Euler-Lagrange equation. The discussion includes some directions to systems modeling and simplification, system metric testing procedures, metric decomposition approaches, and their geometrical and physical interpretations. Since the study is mathematically based on several concepts from classical differential geometry, such as Riemannian metric space, covariant derivative, differential connection, geodesic equation, the Riemann curvature tensor, and geodesic deviation and stability, a brief overview of these fundamental definitions and properties is given. A metric testing problem and a metric decomposition procedure are considered. The geodesic deviation as well as computer iterations to assess Euclidean metrics for given dynamic systems are outlined. The physical and geometrical interpretation of the metric decomposition is described