2080 



Oscillations about Equilibrium 



2090 



Integrable case of equations of motion of 

 system of particles. Richelot, F. J. [1849] 

 Crelle J. 40 (1850) 178-. 



cases of equations of motion of particle. 

 Liouville, J. Liouv. J. Mth. 11 (1846) 345- ; 

 12 (1847) 410-. 



-------- (Liouville). Bertrand, 



J. Liouv. J. Mth. 11 (1846) 379-. 

 ----- point in plane. Elliot, . C. 



E. 116 (1893) 1117- ; Par. EC. Norm. A. 11 



(1894) 9-. 

 Integral more general than that of vis viva for 



system of material points. Pennacchietti, G, 



Mil. I. Lomb. Ed. 18 (1885) 242-, 269-. 

 Integrals of 2nd degree in mechanical problems. 



Liouville, R. C. E. 113 (1891) 838-. 

 -- equations of motion of particle, that are 



linear fractional functions of velocities. 



Vivanti, G. Palermo Cir. Mt. Ed. 6 (1892) 



------- , simplest forms. Bertrand, 



J. Liouv. J. Mth. 2 (1857) 113-. 

 ----- in plane, use of curvilinear co- 



ordinates. Joukovsky, N. E. Liouv. J. 



Mth. 4 (1878) 425-. 

 Integration. Bertrand, J. C. E. 35 (1852) 



698-; Liouv. J. Mth. 17 (1852) 393-. 



. Bour, E. C. E. 40 (1855) 524-; Par. 

 Mm. Sav. Etr. 14 (1856) 792-. 



(Bour). Liouville, J. Liouv. J. Mth. 20 

 (1855) 135-. 



. Massieu, . C. E. 49 (1859) 352-. 



. Graindorge, J. Liege S. Sc. Mm. 16 

 (1890) No. 1, 290 pp. 



of equations of motion of particle under 

 potential forces. Liouville, J. Con. des 

 Temps (1849) 255-. 



------ system of particles. Liou- 



ville, J. Liouv. J. Mth. 14 (1849) 257-. 

 --------- . Bervi, N. V. 



Mosc. S. Sc. Bll. 91 (No. 2) (1895) 32- ; 



Fschr. Mth. (1895) 827-. 

 Problem of analysis relating to equations of 



dynamics. Liouville, E. C. E. 115 (1892) 



403-, 468. 

 Quadratic first integrals. Pirro, G. di. A. 



Mt. 24 (1896) 315-. 



integrals. Staeckel,P. A. Mt. 25 (1897) 55-. 

 -- of Lagrange's equations. Painleve, P. 



C. E. 124 (1897) 221- ; 125 (1897) 156. 

 Variation of constants. Poisson, S. D. [1808] 



Par. EC. Pol. J. 15 e cah. (1809) 266-. 

 --- . Ostrogradsky, M. A. [1829] St. 



Pe"t. Ac. Sc. Mm. 1 (1831) 111-. 

 --- . Cauchy, A. L. Liouv. J. Mth. 2 



(1837) 406-. 

 --- . Binet, J. P. M. Par. EC. Pol. J. 



28 e cah. (1841) 1-. 

 --- . Ostrogradsky, M. A. [1847] St. 



Pet. Ac. Sc. Bll. 7 (1849) 113-. 



2080 Approximate methods. 



Lindstedt's series for solution of 



< jJ2 + n2p=/j.<}>(p,x). Poincare,J.H. C.E. 

 108 (1889) 21-. 



Mechanical integration applied to problem of 

 3 bodies. -.Stromgren, E. Stockh. Ofv. 

 (1900) 443-. 



Periodic orbits. Darwin, G. H. Acta Mth. 21 

 (1897) 99-. 



2090 Oscillations and initial 

 motions about a state of equili- 

 brium. 



Harmonically vibrating particle, kinetic 

 energy. Herschkowitz , J. H. Mth. Gz. 1 

 (1900) 108-. 



Instability of equilibrium in certain cases 

 where force-function is not a maximum. 

 Liapounoff, A. Liouv. J. Mth. 3 (1897) 

 81-. 



Lagrange's "Mecanique Analytique," correc- 

 tion. A., H. J. Silliman J. 11 (1826) 398-. 



Logarithmic decrement, correction formula. 

 Braun, W. Z. Mth. Ps. 25 (1880) 342-. 



MOTIONS. 



Staude, O. Dorpat 

 Dorpat Sb. 8 



conditionally periodic. 



Sb. 8 (1889) 249-. 

 and periodic. Staude, 0. 



(1889) 155-. 

 damped, reduced equations for calculation. 



Curie, P. Lum. Elect. 41 (1891) 201-, 



270-, 307-, 356-. 

 harmonic, graphic compounding. Bazzi, E. 



N. Cim. 22 (1887) 150-. 

 infinitely small, of homogeneous bodies, 



especially plane waves, discovery of integrals 



representing. Cauchy, A. L. C. E. 29 



(1849) 606-. 

 periodic, systems with, theorem. Ronkar, E. 



Brux. Ac. Bll. 8 (1884) 121-. 

 near position of unstable equilibrium. Kneser, 



A. Crelle J. Mth. 115 (1895) 308- ; 118 



(1897) 186- ; Dorpat Sb. 11 (1896) 153-. 

 . Karstens,H. [1898] Dorpat 



Sb. 12 (1901) 66-. 



rolling, fallacy concerning ; small rolling oscil- 

 lations about equilibrium. Korteweg, D. J. 



N. Arch. Wisk. 4 (1899) 130-. 

 small, for one degree of freedom. Elliott, 



E. B. Mess. Mth. 15 (1886) 38-. 

 , of material system in stable equilibrium. 



Lucas, F. C. E. 78 (1874) 1636-. 

 , periodic, of systems. Painleve, P. C. E. 



124 (1897) 1222-. 

 , , of long period. Painleve, P. C. 



E. 124 (1897) 1340-. 

 systematic, of suspended bodies. Lagrange, 0. 



[1894] Ciel et Terre 15 (1894-95) 329-, 



Oscillating constrained system, period-equa- 

 tion. Nanson, E. J. Mess. Mth. 26 (1897) 

 59-. 



system with synchronous pendular con- 

 straint, stability of motion. Cornu,A. Par. 

 S. Ps. S6. (1887) 142-. 



161 



