漫谈Lyapunov稳定性的理论、方法和应用

Talking on the theory,methods and application of Lyapunov stability

根据个人学习研究稳定性的心得体会,首先介绍了前苏联伟大的数学力学家Lyapunov院士的博士论文《运动稳定性的一般问题》在全世界产生的超过1个世纪的巨大影响.叙述了由该博士论文首创的几个巨大成就何以能奠定1门学科的基础,从而开创了1个新的重要的研究方向,以及留给后人很多很多研究的课题的理由.特别地,用事实和科学断语回答了"Lyapunov稳定性已领风骚100多年,余晖还几何"的问题.明确表明1个观点:稳定性将是1个"永恒的主题",不老的科学,定将永恒地给人启迪,洞察力,智慧和思想.

According to individual experience from the study of stability, the doctoral thesis entitled The General Problem of the Stability of Motion by the former Soviet Union academician Lyapunov is first introduced, which has greatly influenced the world over a century. Then this paper describes how the several main contributions the thesis initially made establish foundation for a new subject, inaugurating an important new research direction, and why it can leave many research subjects for later generations. Especially, based on the scientific facts, this paper gives an answer to the question ＂how long the brilliance of Lyapunov stability will continue to last after it has already been influential for over a century＂. A viewpoint is clearly expressed that stability is an eternal theme, and also an immortal subject, which will continuously give people enlightenment, insight, wisdom, and ideas.