FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 2, PAGES 357-377

On two-dimensional integral varieties of a class of discontinuous Hamiltonian systems

V. F. Borisov

Abstract

View as HTML     View as gif image    View as LaTeX source

We consider the following discontinuous Hamiltonian system
\begin{gather*}
\dot y = I \mathop{grad} H(y), \\
H(y)= H_0(y)+u H_1(y), \quad u = \mathop{sgn} H_1(y), \quad I =
\begin{pmatrix}
0 & -E\\
E & 0
\end{pmatrix}.
\end{gather*}
Here $E$ is the unit $(n\times n)$-matrix, $y\in \mathbb R^{2n}$. Under general assumptions, we prove that a vicinity of a singular extremal of order $q$ ($2\le q \le n$) contains $[q/2]$ integral varieties with chattering trajectories. That means that the trajectories enter into the singular extremal at a finite instant with an infinite number of intersections with the surface of discontinuity (Fuller's phenomenon).

All articles are published in Russian.

Main page Contents of the journal News Search

Location: http://mech.math.msu.su/~fpm/eng/k00/k002/k00202t.htm
Last modified: September 1, 2000