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.
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 v2. The equivalent Lagrangian and Hamihonian of each case are shown, and different ways of obtaining the solution, such as first integral,point transformation,canonical transformation and Hamihon-Jacobi equation are discussed.
出处
《大学物理》
北大核心
2006年第10期11-15,共5页
College Physics
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
damped motion of falling body
analytical mechanics
inverse problem of analytical mechanics
equivalent Lagrangian function
non-conservative system
