Safe domain and elementary geometry

Details Safe domain and elementary geometry Safe domain and elementary geometry

2004-10-06

arxiv.org/abs/physics/0410034v1

European Journal of Physics 25 (2004) 835-844

Physics

Physics Education

Also available from http://democrite.in2p3.fr/democrite-00023173

Scientific paper

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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