dorsal/arxiv
View SchemaSafe domain and elementary geometry
| Authors | J. -M. Richard |
|---|---|
| Categories | |
| ArXiv ID | physics/0410034 |
| URL | https://arxiv.org/abs/physics/0410034 |
| Journal | European Journal of Physics 25 (2004) 835-844 |
Abstract
A classical problem of mechanics involves a projectile fired from a given point with a given velocity whose direction is varied. This results in a family of trajectories whose envelope defines the border of a 'safe' domain. In the simple cases of a constant force, harmonic potential and Kepler or Coulomb motion, the trajectories are conic curves whose envelope in a plane is another conic section which can be derived either by simple calculus or by geometrical considerations. The case of harmonic forces reveals a subtle property of the maximal sum of distances within an ellipse.
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"abstract": "A classical problem of mechanics involves a projectile fired from a given\npoint with a given velocity whose direction is varied. This results in a family\nof trajectories whose envelope defines the border of a \u0027safe\u0027 domain. In the\nsimple cases of a constant force, harmonic potential and Kepler or Coulomb\nmotion, the trajectories are conic curves whose envelope in a plane is another\nconic section which can be derived either by simple calculus or by geometrical\nconsiderations. The case of harmonic forces reveals a subtle property of the\nmaximal sum of distances within an ellipse.",
"arxiv_id": "physics/0410034",
"authors": [
"J. -M. Richard"
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"journal_ref": "European Journal of Physics 25 (2004) 835-844",
"title": "Safe domain and elementary geometry",
"url": "https://arxiv.org/abs/physics/0410034"
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