| 阻尼落体运动的分析力学研究 |
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| 引用本文： | 丁光涛.阻尼落体运动的分析力学研究[J].大学物理,2006,25(10):11-15. |
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| 作者姓名： | 丁光涛 |
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| 作者单位： | 安徽师范大学,物理与电子信息学院,安徽,芜湖,241000 |
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| 摘 要： | 应用分析力学理论和方法,研究了两种情况下的阻尼落体运动:1)阻力大小与速度成正比;2)阻力大小与速度平方成正比.对两种运动分别给出了等效的Lagrange函数和Hamilton函数,并应用第一积分法、点变换法、正则变换法和Ham-ilton-Jacobi方程法等不同的求解方法进行了求解.
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| 关 键 词： | 阻尼落体运动 分析力学 分析力学逆问题 等效的Lagrange函数 非保守系统 |
| 文章编号： | 1000-0712（2006）10-0011-05 |
| 收稿时间： | 2006-01-11 |
| 修稿时间： | 2006-06-19 |
Study of the damped motions of falling body in anahytical mechanics |
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| DING Guang-tao.Study of the damped motions of falling body in anahytical mechanics[J].College Physics,2006,25(10):11-15. |
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| Authors: | DING Guang-tao |
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| Institution: | College of Physics and Electronic Information, Anhui Normal University, Wuhu, Anhui 241000, China |
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| Abstract: | By using the theories and techniques of analytical mechanics,the damped motions of falling body are studied in two cases: 1) damping resistance varying as v;2) damping resistance varying as v~(2).The equivalent Lagrangian and Hamiltonian of each case are shown,and different ways of obtaining the solution,such as first integral,point transformation,canonical transformation and Hamilton-Jacobi equation are discussed. |
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| Keywords: | damped motion of falling body analytical mechanics inverse problem of analytical mechanics equivalent Lagrangian function non-conservative system |
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