• 应用研究 •

### 考虑空气阻力和地球自转的远程抛射体的研究

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
• 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

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