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Journal Articles European Journal of Physics Year : 2004

Safe domain and elementary geometry



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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Dates and versions

in2p3-00023173 , version 1 (05-10-2004)



J.-M. Richard. Safe domain and elementary geometry. European Journal of Physics, 2004, 25, pp.835-844. ⟨10.1088/0143-0807/25/6/016⟩. ⟨in2p3-00023173⟩
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