摘要
对于由哈密顿函数H(p,q)描述的一维保守系统,导出了当等能线是绕中心的闭合曲线时,相点始终按顺时针或逆时针方向运动的条件,以及振动的周期与系统的能量之间的关系式,讨论了质点在对称势阱内作周期运动的一类情况,并把谐振子、"xn振子"、单摆及Duffing振子(硬非线性弹簧与软非线性弹簧)作为应用实例.
For onedimensional conservative systems, the condition that closed orbits in the phase plane surrounding the center are clockwise or counterclockwise is deduced and the relation between period and energy of periodic motion is derived. Examples for periodic motions of a particle in symmetric potential wells are given to illustrate application of the theoretical formulas, including harmonic oscillators,'xn oscillators', simple pendulum and Duffing oscillators('soft'and 'hard'nonlinear springs).
出处
《大学物理》
北大核心
2003年第11期3-8,14,共7页
College Physics
关键词
非线性振动
哈密顿系统
周期
能量关系
nonlinear vibration
Hamiltonian system
period versus energy relation
