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levicoFINAL. dvi - Queen Mary University of London Consider a polyhedron P in 3-space We view P as a ‘ panel-and-hinge framework’ in which the faces are 2-dimensional panels and the edges are 1-dimensional hinges
LAGRANGE EQUATIONS AND D’ALEMBERT’S PRINCIPLE The Lagrange equations represent a reformulation of Newton’s laws to enable us to use them easily in a general coordinate system which is not Cartesian Important exam-ples are polar coordinates in the plane, spherical or cylindrical coordinates in three dimensions
CPY Document - Queen Mary University of London 3 4 Fundamental domains for Kleinian groups, Poincaré's polyhedron theorem Let G be a Kleinian group, acting on H3, on C, or on H3 UC, and let 2(G) be the regular set for the action
7 Euler Tours - Queen Mary University of London The proof of Theorem 7 3 is constructive and gives rise to the following polyno-mial algorithm for constructing an Euler tour Suppose G is a connected graph such that all vertices of G have even degree
6 Fundamental domains and examples of Kleinian groups The version for H3 (Poincare's Polyhedron Theorem) is analogous Now the `sides' that are paired by the gs are two-dimensional faces and instead of conditions (i) and (ii) we ask that neighbourhoods of edges of P t together neatly (neighbourhoods of vertices then automatically t together properly)