摘要
为了得到干摩擦问题存在周期解的判断方法,利用微分包含理论对系统+k^2x+μSngp(t)+T(t)a.e.进行了讨论.在周期外力p(t)周期等于固有周期2π/R的情形下得到了周期解存在的充要条件,在周期外力p(t)周期不等于固有周期整数倍2nπ/R的情形下得到了周期解存在的充分条件.
In order to explore a method to judge the existence of periodic solution for dry friction problem, the theory of differential indusion is used to discuss this problem based on the system x+k^2x+μSngx p(t)+ρτ(t) a.e.. the sufficient and necessary condition for the existence of periodic solution is obtained when the period of outside force p(t) is equal to 2π/R, and the sufficient condition for the same problem is also obtained when the period of p(t) is unequal to 2nπ/R.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第21期220-226,共7页
Mathematics in Practice and Theory
基金
教育部科学技术重点项目(209134)
宁夏自然科学基金(NZ1051)
关键词
干摩擦问题
周期解
存在性
dry friction problems
periodic solutions
existence