非保守系统的积分不变量及其在现代物理中的应用

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Integral Invariant in Noncoservative Systems and Its Application in Modern Physics

摘要: 本文导出了非保守系统的庞卡勒-卡当(Poincaré-Cartan)积分不变量和庞卡勒通用积分不变量.并以积分不变量为工具,研究了三度对称螺旋扇回旋加速器中粒子的非线性振动.结果表明,该方法是成功的.

Abstract: In this paper, the Poincaré and Poincaré-Cartan integral invariants in nonconservative systems are established. According to the integral invariant, he non-linear oscillation of particles in 3-folded symmetry spiral sector cyclotron is investigated, It turns out that the method is successful.

[1]	刘成群、徐铭陶,非完整保守系统的积分不变量及其应用,第十六届国际理论及应用力学会议论文,丹麦(1984).
[2]	Vujanovic,B.,A variational principle for nonconservative dynamical systems.Z.Angew.Math.Mech.,55(1975),321.
[3]	甘特马赫,《分析力学讲义》,人民教育出版社(1980).93-96.
[4]	Gordon,M.M.,et al.,Effects of field imperfections on radial stability in a three-sector cyclotron,Nuclear Instruments and Methods,18,19(1962),243.
[5]	Hayashi,C,Nonlinear Oscillation in Physics Systems,McGraw Hill Book Company,New York(1964).

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