空气阻力与地球自转影响下自由落体的运动

Movement of Free-falling Body Affected by air Resistance and Rotation of Earth

讨论自由落体东偏时,同时考虑了空气阻力与地球自转的影响,并结合空气阻力模型建立了相应的落体运动微分方程。忽略二阶小量,依次得到落体的运动规律。最后利用Mathematica编程作出了落体的位移-时间图像,并与忽略阻力时的情形作了对比,定量地说明了在空气阻力与地球自转影响下与忽略空气阻力相比,自由落体的偏东量值变大,此外东偏量值还与质点所在处的纬度有关,纬度越小的地方东偏量值越大,在两极没有东偏量,在赤道处东偏最大。

The eastward drift of free falling body is discussed by considering the air resistance and the impact of the earth rotation simultaneously in this paper.Then combined with air resistance model,the corresponding equations are established.Approximate solutions to these equations are given by ignoring a small amount of second-order,so the movement laws of free-falling body are obtained.In the end,free-falling body′s displacement-time images are drawn with the aid of Mathematica programming,and the images affected by the air resistance and the impact of the earth rotation are contrasted with the images affected by the impact of the Earth′s rotation,which explains that the eastward drift of free falling body is lager affected by the Earth′s rotation and the resistance of air constrasted with that neglecting air resistance.Furthermore,the eastward drift of free falling body has relation with the Earth′s latitude where the body is located.The smaller the latitude is,the larger eastward drift the free falling body will obtain.At the two poles the free falling body doest′t have eastward drift.,but at the equator the free falling body′s eastward drift is maximum.