论文标题
在一个弹丸家族的椭圆形基因座上
On the elliptic locus of a family of projectiles
论文作者
论文摘要
自由落体运动的鲜为人知的属性是由单个点以相同初始速度从单个点发射的Coplanar弹丸达到的最大高度的椭圆形轨迹。另一个鲜为人知的，也许有些令人惊讶的是，该家族的财产在于上述椭圆也是弹丸距离发射点距离的临界点的几何基因座。在文章中，为了更好地了解所涉及的几何形状，我们从自由落下的框架的角度考虑了这些基因座。结果表明，在此参考框架中，所考虑的基因座是一致的圆圈，沿着水平和内部切线与另一个圆形相切，是大圆圈的两倍，代表了弹丸的范围的位置。这种简化的几何描述被用来恢复实验室框架中的椭圆基因座，并进一步探索其特性。
A little known property of free-fall motion is the elliptic locus of the maximum heights attained by coplanar projectiles launched from a single point in different directions with the same initial speed. Another, less known and perhaps somewhat surprising, property of this family consists in the said ellipse being also the geometric locus of the critical points of the projectiles' distances from the launch point. In the article, to gain a better perspective on the geometry involved, we consider these loci from the standpoint of a free-falling frame. It is shown that, in this reference frame, the considered loci are congruent circles tangent to each other along the horizontal and internally tangent to another, twice as big a circle, which represents the locus of the projectiles' ranges. This simplified geometric description is employed to recover the elliptic locus in the laboratory frame and further explore its properties.
