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力学与实践

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考虑空气阻力和地球自转的远程抛射体的研究

王安祥, 张晓军, 翟学军, 常红芳   

  1. 西安工程大学理学院,西安 710048
  • 收稿日期:2012-01-10 修回日期:2012-05-02 出版日期:2012-08-15 发布日期:2012-08-27
  • 通讯作者: 王安祥,副教授,现主要从事力学及理论力学的教学与科研工作. E-mail: waxiang0921@126.com E-mail:waxiang0921@126.com
  • 作者简介:王安祥,副教授,现主要从事力学及理论力学的教学与科研工作. E-mail: waxiang0921@126.com
  • 基金资助:

    陕西省教育厅科研项目(11JK0557), 西安工程大学教育教学改革研究项目(2010JG48) 和陕西省自然科学基金项目(2012JM1011)资助.

RESEARCH ON A REMOTE PROJECTILE CONSIDERING THE AIR RESISTANCE AND THE EARTH ROTATION

WANG Anxiang, ZHANG Xiaojun, ZHAI Xuejun, CHANG Hongfang   

  1. School of Science, Xi'an Polytechnic University, Xi'an 710048, China
  • Received:2012-01-10 Revised:2012-05-02 Online:2012-08-15 Published:2012-08-27

摘要:

针对地球表面坐标系计算远程抛射体落地时间和位置的不足,通过两种方法获得远程抛射体的落地信息. 首先通过在地球表面建立空间直角坐标系计算出考虑空气阻力和地球自转情况下任意抛射角的抛射体的解析解,然后获得了在地球表面所建立的空间直角坐标系与地心坐标系的转换关系式,以抛射体与地心的距离为地球半径作为落地点的条件来计算落地时间和落地位置. 另外,采用球面坐标系表示抛射体的位置、速度及加速度,通过数值计算方法获得抛射体的落地信息. 两种方法所得的结果比较接近,因此两种方法来获得远程抛射体的落地信息都是可行的.

关键词:

抛射体|科里奥利力|龙格-库塔法|空气阻力

Abstract:

Remote projectile landing time and location on the earth's surface were calculated using two ap-proaches, becase of the calculation defects in the rectangular Cartesian coordinate system connected to the earth's surface. First, we established a rectangular Cartesian coordinate system on the earth's surface, and then calculated the analytical solution for arbitrary projection angles considering the air resistance and the earth rotation. The conversion relation between the rectangular Cartesian coordinate system and the geocen-tric coordinate system was obtained. The landing time and location of the remote projectile were calculated under the condition that the distance between the projectile and the earth's core is equal to the earth radius R. Second, the position, velocity and acceleration of the projectile was described in the spherical coordinates system, the landing information of the projectile was obtained by numerical calculation. The calculation results from the two methods are very close, indicating that both the two methods are feasible for obtaining information of the projectile.

Key words:

projectile|Coriolis force|Runge-Kutta method|air resistance

中图分类号: 

  • O313.1