在有心力场中行星运行轨道稳定性的证明

:2003-11-27;:2004-09-13:(1956),,,,.,(,441053):,,:F=-k2m2r-n,n3.:;;:O313.1;O317+.2:A:100020712(2005)0320018202.,r0r,rr0,.?[1].,,,.m,F=F(r)er,Fr,er.,m(r-r2)=F(r)(1)m(r+2Ûr)=0(2)(2)m1rddt(r2)=0m,r2=h(3)h.(3)(1)r-h2r-3=1mF(r)(4),(4).x=r,y=r,(4)x=y(5)y=1mF(x)+h2x-3(6)(5)(6),x=0,y=0,x0=-mh2F(x0)1/3,y0=0,.,.,J=5x5x5x5y5y5x5y5y=010(7)=1mF(x0)-3h2x-40(8),J=(9)(9),J-=0(10)0-10-=2-=0==1mF(x0)-3h2x-40[2],0,,..,[3].0,1mF(x0)3h2x-40(11)243Vol.24No.320053COLLEGEPHYSICSMar.2005©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(n0),F(x)=-k2mxn(12)(11)x3-n03h2nk2(13),1m-k2mxn0+h2x-30=0,x3-n0=h2k2(14)(14)(13)n3.[(12)],n3.[1].(n=2),,..,,.,,.:[1].[M].2.:,1985.83.[2],,.[M].:,2001.11.[3].[M].:,2002.32.StabilityofplanetorbitsincentralfieldYANGDe2jun,XIAQing2hua(DepartmentofPhysics,XiangfanUniversity,Xiangfan,Hubei441053,China)Abstract:Basedonthebasicmotionequation,thestabilityoftheplanetorbitsincentralfieldisstudiedus2ingnonlineardynamicsmethod.Wegettheconditionofstabilityofplanetorbitsincentralfieldisn3.Keywords:nonlineardynamicsmethod;orbitstability(17)AcalculationforperiodofasinglefreedomnonlinearconservativesystemRENBao2wen,ZHENGYa2e(DepartmentofPhysics,XidianUniversity,Xipan710071,China)Abstract:Acalculationforperiodofasinglefreedomnonlinearconservativesystemvibratinginalargeam2plitudeisperformed,andtheperiodformulaeofsometypicalvibrationproblemsarepresented.Keywords:nonlinearconservativesystem;seriesexpansion;numericalapproximation;Mehlerformula;inte2grationformulaofperiodicalfunction;formulaofvibrationperiod3:19©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.