dorsal/arxiv
View SchemaFrom circular paths to elliptic orbits: A geometric approach to Kepler's motion
| Authors | A. González-Villanueva, E. Guillaumín-España, R. P. Martínez-y-Romero, H. N. Núñez-Yépez, A. L. Salas-Brito |
|---|---|
| Categories | |
| ArXiv ID | physics/9810034 |
| URL | https://arxiv.org/abs/physics/9810034 |
| DOI | 10.1088/0143-0807/19/5/004 |
| Journal | Eur. J. Phys. vol 19 (1998) 431-438 |
Abstract
The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.
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"abstract": "The hodograph, i.e. the path traced by a body in velocity space, was\nintroduced by Hamilton in 1846 as an alternative for studying certain dynamical\nproblems. The hodograph of the Kepler problem was then investigated and shown\nto be a circle, it was next used to investigate some other properties of the\nmotion. We here propose a new method for tracing the hodograph and the\ncorresponding configuration space orbit in Kepler\u0027s problem starting from the\ninitial conditions given and trying to use no more than the methods of\nsynthetic geometry in a sort of Newtonian approach. All of our geometric\nconstructions require straight edge and compass only.",
"arxiv_id": "physics/9810034",
"authors": [
"A. Gonz\u00e1lez-Villanueva",
"E. Guillaum\u00edn-Espa\u00f1a",
"R. P. Mart\u00ednez-y-Romero",
"H. N. N\u00fa\u00f1ez-Y\u00e9pez",
"A. L. Salas-Brito"
],
"categories": [
"physics.class-ph",
"physics.ed-ph"
],
"doi": "10.1088/0143-0807/19/5/004",
"journal_ref": "Eur. J. Phys. vol 19 (1998) 431-438",
"title": "From circular paths to elliptic orbits: A geometric approach to Kepler\u0027s motion",
"url": "https://arxiv.org/abs/physics/9810034"
},
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