The calculus of variations and the forced pendulum
The calculus of variations and the forced pendulum
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变分法和受迫摆
DOI：
10.1007/978-1-4020-6964-2_15
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
P. Rabinowitz
中科院分区：
文献类型：
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作者：
P. Rabinowitz
考虑受迫摆型方程：U“+Vu(t，u)=0(*)，其中‘=d/dtandV是光滑的，它的变元是1-周期的。我们将展示如何利用初等极小化变元来寻找(*)的各种解。我们从(*)的周期解入手，然后找出在两个周期之间有一个过渡的异宿解。然后我们构造异宿和同宿，使得周期之间有多次(甚至无穷多个)过渡。如果时间允许，我们还可以讨论(*)的相关山路轨道的构造。
Consider the equation of forced pendulum type:u"+Vu(t,u) = 0 (*) where' =d/dtandVis smooth and 1-periodic in its arguments. We will show how to use elementary minimization arguments to find a variety of solutions of (*). We begin with periodic solutions of (*) and then find heteroclinic solutions making one transition between a pair of periodics. Then we construct heteroclinics and homoclinics making multiple (even infinitely many) transitions between periodics. If time permits, we may also discuss the construction of related mountain pass orbits of (*).