Previous |  Up |  Next


fibred manifold; Lagrangian; Lepage form; conservation laws; relativistic mechanics
In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred manifold with one-dimensional base to the relativistic mechanics. Using this geometrical theory, we obtain and discuss some well-known conservation laws in their general form and apply them to a concrete physical example.
[1] Krupka, D.: Global variational theory in fibred spaces. Handbook of global analysis (Krupka, D., Saunders, D., eds.), Elsevier, 2007, pp. 773–836. MR 2389646
[2] Krupková, O.: Mechanical systems with non-holonomic constraints. J. Math. Phys. 38 (1997), 5098–5126. DOI 10.1063/1.532196 | MR 1471916
[3] Krupková, O.: The Geometry of Ordinary Variational Equations. Lecture Notes in Math., vol. 1678, Springer, Berlin, 1997. MR 1484970
[4] Krupková, O., Musilová, J.: The relativistic particle as a mechanical system with non-holonomic constraints. J. Phys. A: Math. Gen. 34 (2001), 3859–3875. DOI 10.1088/0305-4470/34/18/313 | MR 1840850
[5] Musilová, J., Lenc, M.: Lepage forms in variational theories: From Lepage’s idea to the variational sequence. Variations, Geometry and Physics (2008), 1–31, O. Krupková and D. Saunders (Editors). Nova Science Publishers. MR 2523430
[6] Weinberg, S.: Cosmology. Oxford University Press, 2008. MR 2410479 | Zbl 1147.83002
Partner of
EuDML logo