Trajectories and lines of force
| Autor: | Aaron Fialkow |
|---|---|
| Rok vydání: | 1935 |
| Předmět: | |
| Zdroj: | Transactions of the American Mathematical Society. 38:89-105 |
| ISSN: | 1088-6850 0002-9947 |
| Popis: | In this paper we generalize certain theorems of Kasnert relative to the geometry of arbitrary fields of force in the plane. Consider the motion of a particle which starts from rest in a positional field of force at a point where the force does not vanish. It begins to move along the line of force on which it is situated. However, due to the effect of inertia, it does not remain on this line of force, but travels in a somewhat straighter path. In general, the line of force and the trajectory will have the same initial direction but different initial curvatures. Kasner has shown that the curvature of the trajectory is always one-third the curvature of the line of force. If the initial curvature of the line of force vanishes, this result, while still valid, is not significant. In this case Kasner studies the ratio between the infinitesimal departures of the path and the line of force from their common tangent line. He proves the following theorem |
| Databáze: | OpenAIRE |
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