By Frank K. Edmondson (auth.), S. Flügge (eds.)
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Example text
12) become identical with the results of Sects. 7 and 8, if we put hj=O and Gik=O, when one of the indices i, k=4=O. Among the stream coefficients ~oo, [lo02' ~Ol' V002 , Von, moo, Wo20' Wo02' ~IO' ~Ol' Won, vanish. g. 12 and ms , are 21 in principle observable quantities whithin the local region which may serve for the determination of the 20 parameters 0'1,0'2,0'3' HECKMANN and STRASSL apply an analysis in accordance with their stream formula to the results obtained by MINEUR and GUINTINI I for the two-dimensional streaming parallel to the galactic plane of the B stars in our surroundings.
5. BERTlL LINDBLAD: Galactic Dynamics. 6) . This partial differential equation is equivalent with dt _ dx _ dY _ - U - V dz _ dU _ - W - dV Of{! - _ dW }rp . }f{! 7) OZ These are the equations of motion. If I 1 =const, 12 = const, ... 8) = F(I1 ,I2' ... , Is), where F is an arbitrary function. This consequence of LIOUVILLE'S theorem was first proved by POINCARE 1. It was established by JEANS as a basis for stellar dynamics in 1915 (Sect. 1). A specification of all the six integrals would mean a detailed description of the actual motions in the system.
Solving the twenty partial differential equations determining the coefficients of the velocity ellipsoid, the iJ quantities OI the mean motions, and the potential, CHANDRASEKHAR performed a complete survey of the general problem of ellipsoidal distributions with differential motions, including both the steady and nonsteady states. In addition to the monograph [3J the preceding papers [lJ and [2] contain a wealth of theoretical results. We only mention the discussion of the case which is of importance for the problem of the evolution and stability of ellipsoidal systems ([2], pp.