The Geometry of Forces Along Equidistant Particle Paths
Assume that two particles on the sphere leave the equator moving due south and travel at a constant and equal speed along a geodesic colliding at the south pole. An observer who is unaware of the curvature of the space will conclude that there is an attractive force acting between the particles. On...
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| Format: | Text |
| Language: | English |
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.502.2205 http://www.ux1.eiu.edu/~ggalperin/papers/pforce.pdf |
| Summary: | Assume that two particles on the sphere leave the equator moving due south and travel at a constant and equal speed along a geodesic colliding at the south pole. An observer who is unaware of the curvature of the space will conclude that there is an attractive force acting between the particles. On the other hand, if particles travel at the same speed (initially parallel) along geodesics in the hyperbolic plane, then the particle paths diverge. Imagine two particles in the hyperbolic plane that are bound together at a constant distance with their center of mass traveling along a geodesic path at a con-stant velocity, then the force due to the curvature of the space acts to break the bond and increases as the velocity increases. We will give the formula for the apparent force between the particles induced on 2 dimensional space forms of non-zero curvature. AMS classification: 53A; 70E; 85. |
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