2060 Cyclical Systems 



Kinetic energy not integrating divisor of energy 

 absorbed, cases. Boltzmann, L. Wien Ak. 

 Sb. 92 (1886) (Ab. 2) 853-. 



Monocyclic and similar systems, properties. 

 Boltzmann, L. [1884] Wien Ak. Sb.90 (1885) 

 (Ab. 2) 231- ; Crelle J. Mth. 98 (1885) 68-. 



systems, Helmholtz's theorem, new proof. 

 Boltzmann, L. Gott. Nr. (1886) 209-. 



; statics. Helmholtz, H. von. Berl. Ak. 



Sb. (1884) 159-, 311-, 755-, 1197- ; Crelle 



J. Mth. 97 (1884) 111-, 317-. 

 Motion of system with internal variable 



motions. Volterra, V. Em. B. Ac. Line. 



Bd. 4 (1895) (Sem. 2) 107-. 

 Rotation of body containing cyclic systems. 



Volterra, V. Bm. E. Ac. Line. Bd. 4 (1895) 



(Sem. 2) 93-, 350. 



polycyclic systems. Volterra, V. 

 A. Mt. 24 (1896) 29-. 



Variations of latitude. Volterra, V. Acta 

 Mth. 22 (1899) 201-. 



2060 Properties of the integrals, 

 reciprocal relations, periodic 

 solutions. 



Application of theory of complex variable. 



Stankevic, I. V. Bee. Mth. (Moscou) 19 



(1897) 586 (bis)-. 

 Bertrand's relations generalised. Brioschi, F. 



Tortolini A. 4 (1853) 395-. 

 Determinantal invariant. Bryan, G. H. L. 



Ps. S. P. 13 (1895) 481- ; Ph. Mg. 39 (1895) 



531-. 

 Dynamical law of Poincare". Boltzmann, L. 



Wien Ak. Sb. 106 (1897) (Ab. 2a) 12-. 

 Equations integrable by complex quantities. 



Nekrasov, P. A. Bee. Mth. (Moscou) 18 



(1896) 728-; Fschr. Mth. (1896) 271, 272-, 

 609-. 



Force function in 3 variables admitting quad- 

 ratic integral. Levi-Civita, . C. B. 124 



(1897) 1434-. 



Integral, first, of equations with two variables 

 and homogeneous potential function, pro- 



BEbert, W., <& Perchot, J. C. B. 127 

 657-. 

 3. Painleve, P. C. E. 114 (1892) 

 1168-. 

 , algebraic. Koenigs, G. C. B. 103 (1886) 



460-. 



, . Levi-Civita, T. Tor. Ac. Sc. At. 31 

 (1895) 484- or 816-. 



of general equations. Ostrogradsky, M. A. 

 [1848] St. Pet. Ac. Sc. Bll. 8 (1850) 33-. 



linear in respect to velocity, property. 

 Cerruti, V. Bm. B. Ac. Line. Ed. 4 (1895) 

 (Sem. 1) 283-. 



, quadratic. Pirro, G. di. C. B. 123 (1896) 



1054-. 

 , . Levi-Civita, . C. B. 124 (1897) 



392-. 

 , (Levi-Civita). Appell, . C. E. 124 



(1897) 395. 

 , skew symmetric, property. Brioschi, F. 



Tortolini A. 6 (1855) 430-. 



Integral Relations 2070 



Motions and real trajectories of systems. 

 Painleve, P. Par. S. Mth. Bll. 22 (1894) 



Periodic motions, asymptotic, existence in 

 Hess's example. Mlodzeevskij, B. K., 

 & Nekrasov, P. A. Mosc. S. Sc. Bll. 83 

 (No. 1) (1893) 43- ; Fschr. Mth. (1893-94) 

 1439. 



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

 (1897) 99-. 



solutions in case of problem of 3 bodies. 

 Perchot, J., <& Mascart, J. C. B. 120 (1895) 

 906-. 



and least action. Poincare, H. C. B. 



123 (1896) 915- ; 124 (1897) 713-. 

 of problem of motion of heavy body sus- 

 pended at point. Koenigs, G. C. B. 122 



(1896) 1048-. 

 rotation of solid about fixed 



point. Kobb, G. Toul. Fac. Sc. A. 1 (1899) 



5-. 

 Poisson's theorem. Marcolongo, E. Nap. Bd. 



27 (1888) 419-. 

 on constancy of functions of differential 



coefficients of two integrals with respect to 



coordinates. Laurent, H. Liouv. J. Mth. 



17 (1872) 422-. 

 , integrals of system of particles. Liou- 



ville, J. Liouv. J. Mth. 5 (1840) 351-. 

 Beciprocal theorems. Lamb, H. L. Mth. 



S. P. 19 (1889) 144-. 

 Tautochrone problem, reduction to integration 



of partial differential equation of 1st order 



and 2nd degree. Koenigs, G. C. E. 116 



(1893) 966-. 

 Trajectories in dynamics, properties. Hada- 



mard, . Liouv. J. Mth. 3 (1897) 331-. 



Transformation of S rg a rs - . ; recipro- 

 city law. Beltrami, E. [1866] * G. Mt. 5 

 (1867) 24-. 



2070 Methods for the actual 

 determination of exact integrals. 



Connected particles, system under forces with 



potential. Morera, G. Mil. I. Lomb. Bd. 



15 (1882) 537-. 

 Dynamical problems, class, and geodesic lines. 



Staeckel, P. C. E. 116 (1893) 485-. 

 which reduce to quadratures. Staeckel, 



P. C. B. 116 (1893) 1284-. 

 Equations, finite, of permanent motion of 



system. Formenti, C. G. Mt. 15 (1877) 



268-. 

 First integrals of equations of motion . Pennac- 



chietti, G. Catania Ac. Gioen. At. 3 (1891) 



67-. 



Forces functions of coordinates only, case ad- 

 mitting of quadratures. Jacobi, C. G. J. 



[1842-43] C.B. 15(1842)202-; St. Pet. Ac. 



Sc. Bll. 3 (1845) 33-. 

 Hamilton's equations, reduction to 2n-2 



canonical equations and quadrature. Siacci, 



F. Tor. Ac. Sc. At. 15 (1879) 809. 



160 



