Skip to Main content Skip to Navigation
Journal articles

Safe domain and elementary geometry

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.
Complete list of metadata

http://hal.in2p3.fr/in2p3-00023173
Contributor : Lpsc Bibliotheque Connect in order to contact the contributor
Submitted on : Tuesday, October 5, 2004 - 11:22:05 AM
Last modification on : Thursday, November 19, 2020 - 12:58:27 PM
Long-term archiving on: : Thursday, April 1, 2010 - 3:17:09 PM

Identifiers

Collections

LPSC | CNRS | IN2P3 | GEPI | UGA

Citation

J.-M. Richard. Safe domain and elementary geometry. European Journal of Physics, European Physical Society, 2004, 25, pp.835-844. ⟨in2p3-00023173⟩

Share

Metrics

Record views

332

Files downloads

539