Safe domain and elementary geometry

J. -M. Richard

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arXiv · physics/0410034

Safe domain and elementary geometry

J. -M. Richard

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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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J. -M. Richard. 2004-10-06. Safe domain and elementary geometry. https://arxiv.org/abs/physics/0410034

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