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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Higher-dimensional Einstein gravity
 Štrupl, František ; Podolský, Jiří (advisor) ; Pravda, Vojtěch (referee)
In the present work, we study some aspects of Einstein's theory of gravitation in general spacetimes with an arbitrary number of dimensions. In the first chapter we summarize the foundations of used geometric formalism and we derive the equation of goedesic deviation representing the relation between relative acceleration and the Riemann tensor. Second chapter presents different types of algebraic classification of the Weyl tensor in four and higher dimensions. Third chapter is devoted to a detailed examination of the test particle motions and also to the interpretation of different terms in the general equation of geodesic deviation. The fourth section examines appropriate choice of the interpretation frame and the coordinates. The final fifth chapter contains an analysis of the motion of test particles in the Robinson-Trautman spacetime with an arbitrary higher number of dimensions.
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Geometric formulation of Lagrangian mechanics
 Štrupl, František ; Podolský, Jiří (advisor) ; Krtouš, Pavel (referee)
In the present work we study application of differential geometry to the Lagrangian formalism. In the first chapter we summariz e the foundations of geometric formulation of Lagrangian mechanics,in particular eshow the principal meaning of the tagent bundle of the configuration mani-fold and dynamical vector field which solves the Lagrange equations in theirgeometrical form. The Noether's theorem is also formulatedand proved. The second chapter introduces other geometrical definitions related to theLagrangian formalism, such as fiber space, lifts, second-order vector fieldsand Lagrangian vector fields. The existence of symplectic structure and Hamiltonian dynamics on the tangent bundle of the configuration manifold is also demonstrated. Powered by TCPDF (www.tcpdf.org)
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