On Properties of Torsional Metric Spaces
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, t...
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| 格式: | Artículo |
| 语言: | en_US |
| 出版: |
2018
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| 在线阅读: | https://doi.org/10.4236/jmp.2018.99113 https://www.scirp.org/journal/PaperInformation.aspx?PaperID=86543 |
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| 总结: | 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. |
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