From a dynamical system of the knee to natural jet geometrical objects

TL;DR

This paper develops geometric objects on the 1-jet space derived from a knee motion dynamical system, linking differential geometry with biomechanical modeling and analyzing associated energy surfaces.

Contribution

It introduces a geometric framework on jet spaces based on a knee motion model, connecting dynamical systems with advanced geometric structures.

Findings

Construction of nonlinear and linear connections on jet space

Definition of a jet electromagnetic field and Yang-Mills energy

Analysis of energetic surfaces related to knee dynamics

Abstract

In this paper we construct some natural geometrical objects on the 1-jet space J^1(R,R^3), like a nonlinear connection, a Cartan linear connection (together with its d-torsions and d-curvatures), a jet "electromagnetic" d-field and its geometric "electromagnetic" Yang-Mills energy, starting from a given dynamical system governing the three-dimensional motion of the knee in the mathematical model introduced by Grood and Suntay. The corresponding Yang-Mills energetic surfaces of constant level (produced by this knee dynamical system) are studied.