2020 



Equations of Motion 



2030 



Normal variables, Lipschitz's general theorems. 



Cayley, A. QJ. Mth. 12 (1873) 346-. 

 Periodic motion of finite conservative system. 



Thomson, (Sir) W. Ph. Mg. 32 (1891) 375-. 



motions of system, influence of friction and 

 internal forces. Application to the Earth. 

 Ronkar, E. Brux. Mm. Cour. 4, 51 (1889) 

 No. 1, 55 pp. 



Principle of d'Alembert, and Lagrange's 

 method. Verdam, G. J. [1860] Amst. Vh. 

 Ak. 10 (1864) 90 pp. 



Principles of rational mechanics. Pasquier, . 

 Brux. S. Sc. A. 19 (1895) (Pt. 1) 46-. 



PROBLEM OF 3 BODIES. 



Piltz, A. D. Mth. Vr. Jbr. 1 (1892) 68-. 

 Charlier, C. V. L. Stockh. Ak. Hndl. Bh. 18 



(Afd. 1) (1893) No. 6, 22 pp. ; 19 (Afd. 1) 



(1894) No. 2, 29 pp. ; Fschr. Mth. (1893-94) 



1408-. 

 canonical equation. Siacci, F. C. E. 119 



(1894) 1189. 



equations, transformation. Vernier, P. 

 C. B. 119 (1894) 451-, 503. 



and equations of dynamics. Poincare, E. 



Acta Mth. 13 (1890) 270-. 

 general form of elliptic elements. Zeipel, H. 



von. Stockh. Ak. Hndl. Bh. 24 (Afd. 1) 



(1899) No. 8, 51 pp. 

 periodic solutions, direct calculation. Kobb, G. 



Stockh. Ofv. (1895) 215-. 

 Poincare^'s case, dynamical problems con- 

 nected with. Phragmen, E. Stockh. Ak. 



Hndl. Bh. 15 (Afd. 1) (1890) No. 13, 33 pp. ; 



Fschr. Ps. (1890) (Ab. 1) 262-. 

 simplified. Charlier, C. V. L,. Stockh. Ofv. 



(1899) 263-. 

 special case. Gylden, H. Stockh. Ofv. (1889) 



43-. 



(2 equidistant from third). Fransen, 

 A. E. Stockh. Ofv. (1895) 783-; Fschr. 

 Mth. (1895) 1098. 



Problem of 4 bodies, class of solutions. 

 Moulton, F. R. N. Y. Am. Mth. S. T. 1 



(1900) 17-. 



n bodies, analytical solution . Dillner, G. 



Ups. S. Sc. N. Acta 16 (1893) No. 2, 28 pp. 

 and first integrals of dynamics. 



Painleve, P. C. B. 124 (1897) 173-. 

 , integration of equations. Dillner, 



G. Stockh. Ofv. (1886) 173-, 217- ; (1888) 



367-; (1889)239-. 

 , straight line solutions. Moulton, 



F. R. [1900] N. Y. Am. Mth. S. Bll. 7 



(1901) 244, 249-. 



, transformation of equations. 



Allegret, A. C. B. 79 (1874) 656-. 

 mutually attracting particles. Krediet, 



G. N. Arch. Wisk. 19 (1892) 66- ; Fschr. 

 Ps. (1892) (Ab. 1) 238-. 



Problems depending on 3 quantities reducible 

 to quadratures. Marcolongo, R. Palermo 

 Cir. Mt. Ed. 2 (1888) 193-. 



Eelative motion. Bour, E. [J. E. E.~] Liouv. 

 J. Mth. 8 (1863) 1-. 



Eelative motion. Onnes, H. K. N. Arch. 



Wisk. 5 (*1879) 58-, 135- ; 6 (*1880) 173-. 

 . London, J. Am. J. Mth. 3 (1880) 



174-. 

 . Chessin, A. S. [1895-99] J. H. Un. 



Cir. [14 (1894-95)] 36-; N. Y. Am. Mth. 



S. T. 1 (1900) 116-. 

 , form of equations. Legoux, A. Toul. 



Fac. Sc. A. 8 (1894) I, 20 pp. 



and Lagrange's equations. Gilbert, 

 L. P. [1878-79] As. Fr. C. E. 7 (1878 

 147- ; (xn) Brux. S. Sc. A. 3 (1879) (Pt. 1) 

 58-, 70-, 81- ; 4 (1880) (Pt. 1) 53-. 



. Astor, A. Bll. Sc. Mth. 15 



(1891) 255-. 



motions, theory. Padova, E. A. Mt. 12 

 (*1883-84) 265-. 



Eolling motions, equations analogous to 

 Lagrange's. Appell, P. C. E. 129 (1899) 

 317-. 



, , general. Hadamard, . C. E. 118 



(1894) 911-. 



Eotation problem of Mme. Kovalevski. Kotter, 

 F. D. Mth. Vr. Jbr. 1 (1892) 65-. 



of solid, perturbations. Cayley, A. [1860] 

 As. S. Mm. 29 (1861) 307-. 



Stackel's theorem, deduction. Seiliger, D. N. 

 Kazan S. Ps.-Mth. Bll. 3 (1893) 147-. 



on (ra-1) integrals, generalisation. 

 Burgatti, P. Palermo Cir. Mt. Ed. 9 (1895) 

 125-. 



System of variable form, acceleration in. 



Durrande, H. Par. EC. Norm. A. 3 (1874) 



151-. 

 , kinetics. Durrande, H. C. E. 80 



(1875) 877-. 

 Tautochronism in material system. Appell, P. 



C. E. 114 (1892) 996-. 

 Thermo - mechanical phenomena, equation 



^J^-Vxf'x^dx. Liouville,J. Liouv. 

 dt dx* Jo dt 



J. Mth. 2 (1837) 439- ; C. E. 5 (1837) 598-. 

 Trajectories defined by their tangents. 



Koenigs, G. Par. S. Phlm. Bll. 5 (1893) 



28-. 

 Transformation of motion, case. Dautheville, 



. C. E. Ill (1890) 877-. 

 , . Appell, P. Am. J. Mth. 17 



(1895) 1-. 



Transformations. Painleve, P. C. E. 114 



(1892) 901-, 1104-, 1412-. 



2030 Applications of the first 

 variation of integrals ; the par- 

 tial differential equations. 



(See also 0820.) 



Brachistochrone problem of a system. Webb, 



R. R. Mess. Mth. 9 (1880) 151-. 

 Canonical equations of motion, fundamental 



theorem. Morera, G. Mil. I. Lomb. Ed. 15 



(1882) 640-. 

 Dynamics, reciprocity, law. Siacci, F. Tor. 



Ac. Sc. At. 15 (1879) 519-. 



157 



