Abstract

Relativistic generalisation of the Lenz vector (II) The Lenz vector A = m {*' x L + a • x/r} is a special integral of motion of the non-relativistic Kepler problem. Accordingly, there also exists a special integral of motion A (x, x') of the rela tivistic Kepler problem as pointed out in Part I of this paper. In the following Part II, the system of equations is compiled to the extent required for the relativistic generalisation of the Lenz vector and its interpretation. Starting point are the statements of conservation for the energy and the angular momentum. From these two quantities, it is possible to derive the complete system of solutions x(t) in accordance with standardised methods. Some details and some modifications of the approach are of special importance for the purposes of this paper. In the centre of the consideration are the construction and interpretation of the standardised polar angle Ö as a function of r, r'. The explicit time dependance of the functions r(t), 0(t) is not required for constructing the relativistic Lenz vector in the form A (x, x'). In the literature, one does Find only few, not sufficient for our purposes, data on the relativistic orbits (rosettes, spirals, hyperbola-type curves etc.). It is, therefore, necessary to discuss these orbits in detail. For this purpose, a series of relationships are derived which apparantly have not been published before.