2016/04/16 by R. Ya. Matsyuk · 1 citation
Physics and Astronomy · Mathematics · #physics.class-ph #gr-qc #math.DG #msc:53B50 #msc:49S05 #msc:49N45 #msc:70G65 #msc:70H50 #msc:83A05 #msc:70E99
published as Ukraïn. Fīz. Zh. v. 48 (2003) no. 4 p. 341-349 · Typos corrected. Considerations of Section 5 have been elaborated in more detailes
arxiv created 2016/04/16 · arxiv updated 2016/04/29
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The main goal is to introduce a combined approach consisting in the simultaneous utilization of symmetry principles along with the inverse variational problem considerations in terms of vector-valued differential forms. Next, some simple algorithm of transition between the autonomous variational problem and the variational problem in parametric form is established. The example definitely solved shows no-existence of a globally and intrinsically defined Lagrangian for the Poincaré-invariant and well defined unique variational equation in the case in hand. Hamiltonian counterpart is briefly discussed in terms of Poisson bracket. The model appears to provide a generalized canonical description of the quasi-classical spinning particle governed by the Mathisson-Papapetrou equations in flat space-time.