Search results for "Local coordinates"

showing 2 items of 2 documents

Classical Chern–Simons Mechanics

2001

We are interested in a completely integrable Hamiltonian system \((\mathscr{M}_{2N},\omega,H).\) Local coordinates on the 2N-dimensional phase space \(\mathscr{M}_{2N}\) are denoted by η a = (p, q), a = 1, 2, … 2N and the symplectic 2-form ω is given by

PhysicsPoisson bracketIntegrable systemPhase spaceLocal coordinatesChern–Simons theoryGauge theoryMathematical physicsHamiltonian systemSymplectic geometry
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Regular k-Surfaces

2012

Roughly speaking, a regular surface in \(\mathbb{R}^3\) is a two-dimensional set of points, in the sense that it can be locally described by two parameters (the local coordinates) and with the property that it is smooth enough (that is, there are no vertices, edges, or self-intersections) to guarantee the existence of a tangent plane to the surface at each point.

Set (abstract data type)PhysicsSurface (mathematics)CombinatoricsLocal coordinatesTangent spacePoint (geometry)Tangent vectorSense (electronics)Implicit function theorem
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