Author(s)

Hector Alejandro Trejo-Mandujano¹, George H. Goedecke²

¹Universidad Autónoma de Ciudad Juárez, Chihuahua, México.
²Physics Department, New Mexico State University, Las Cruces, NM, USA.

We apply general tensor calculus to arbitrary nonrelativistic classical Lagrangian systems and derive general relationships between the torsion tensor and other quantities associated with the coordinate configuration space, such as the metric, the Christoffel symbols, the Euler-Lagrange equations, the affine connections, and the curvature tensor. Using Euler angle metric spaces as examples of spaces with nonzero torsion, we calculate these quantities for nonrelativistic rigid rotators of arbitrary structure. For free rotations, we show that the Euler-Lagrange equations agree with the manifestly correct Euler equations.

Torsion, Rigid Rotators, Euler Angle Metrics

Trejo-Mandujano, H. and Goedecke, G. (2018) On Properties of Torsional Metric Spaces. Journal of Modern Physics, 9, 1793-1806. doi: 10.4236/jmp.2018.99113.