A derivation of the Jacobi identity in classical mechanics.
Jacobi identity in classical mechanics
Epstein, S. T.↗
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The topology of the regularized integral surfaces of the 3-body problem.
A method is described by which the integral surface can be modified in such a way that Newton's equations of motion actually give a flow. The process of regularization of vector fields by surgery, as described by the author (1971) is reviewed. The planar 3-body problem and its regularization, and the topology of the integral surfaces are considered. The Lagrange-Jacobi identity is used to show that there exists an isolating block such that any orbit which ends in a triple collision must enter and remain in this block.
Easton, R.↗
Conformal invariance and Hamilton Jacobi theory for dissipative systems
For certain dissipative systems, a comparison can be made between the Hamilton-Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton-Jacobi theory.
Kiehn, R. M.↗
Ellipsoidal figures of equilibrium - Compressible models
The results of Chandrasekhar (1969) are generalized to polytropes, using a formalism based on ellipsoidal energy variational principle to construct approximate stellar equilibrium solutions and study their stability. After reviewing the energy variational method and describing the approach, several equivalent stability conditions are established and secular vs. dynamical instabilities are discussed. Then, the equilibrium structure equations are derived for isolated, rotating polytropes, and axisymmetric configurations (compressible Maclaurin spheroids) are considered. Particular attention is given to triaxial configurations, either in a state of uniform rotation (generalizing the classical Jacobi ellipsoids) or with internal fluid motions of uniform vorticity (the compressible analogues of Riemann-S ellipsoids) and to the stability of these single star configurations. The compressible generalizations of the Roche and Roche-Riemann problems for a polytrope in orbit about a point-mass companion are solved, and the generalized Darwin problem for two identical polytropes in a binary is considered.
Lai, Dong↗
The nova rate in the elliptical component of NGC 5128
The results are presented of a five year nova survey of NGC 5128 performed with an H-alpha filter at the prime focus of the CTIO 4 m telescope. In all, 16 novae were detected, of which 12 are members of a statistically complete and homogeneous sample unaffected by the absorption lane of the galaxy. When normalized to B luminosity, the nova rate in the elliptical component of NGC 5128 is 2.7 + or - 1.0 times less than that observed in the bulge of M31. However, when normalized in the infrared K bandpass, the two nova rates are identical, and comparable to that measured in the Large Magellanic Cloud. These data suggest that (1) the percentage of binary stars is approximately constant over a large range of star-forming environments, (2) the nova rate in our own galaxy is between 11 and 46/yr, and (3) nova rates are not strongly affected by tidal captures in bright globular clusters.
Ciardullo, Robin↗
Simulation fidelity of a virtual environment display
We assessed the degree to which a virtual environment system produced a faithful simulation of three-dimensional space by investigating the influence of a pitched optic array on the perception of gravity-referenced eye level (GREL). We compared the results with those obtained in a physical environment. In a within-subjects factorial design, 12 subjects indicated GREL while viewing virtual three-dimensional arrays at different static orientations. A physical array biased GREL more than did a geometrically identical virtual pitched array. However, addition of two sets of orthogonal parallel lines (a grid) to the virtual pitched array resulted in as large a bias as that obtained with the physical pitched array. The increased bias was caused by longitudinal, but not the transverse, components of the grid. We discuss implications of our results for spatial orientation models and for designs of virtual displays.
Nemire, Kenneth↗