•DensityandPotentialareStaticandAxisymmetric–independentoftimeandazimuthalanglezgRgzRRRRGzRzRzr 2241),(),(Orbitsinanaxisymmetricpotential•Letthepotentialwhichweassumetobesymmetricabouttheplanez=0,be (R,z).•Thegeneralequationofmotionofthestaris•Eqs.ofmotionincylindricalcoordinates),(22zRdtrd Eq.of...
The Laplacian in cylindrical coordinates: > SetCoordinatescylindricalr,θ,z cylindricalr,θ,z (5) > Laplacianfr,θ,z ∂∂rfr,θ,z+r∂2∂r2fr,θ,z+∂2∂θ2fr,θ,zr+r∂2∂z2fr,θ...
The following table gives the form of the Laplacian in several common coordinate systems. coordinate system Cartesian coordinates cylindrical coordinates parabolic coordinates parabolic cylindrical coordinates spherical coordinates The finite difference form is (6) For a pure radial function , ...
An equivalent complex-valued equation in cylindrical symmetric coordinates is obtained by the Hasimoto transformation. A renormalization for the Laplacian is used to transform this equivalent system to a Ginzberg–Landau type system in which the Strichartz estimate can be applied. The global H 2 $H^...
For the cylindrical region, (2.4)-(2.5) consists of the mixed problem, also known as parabolic equations with the initial boundary values. Now, if we consider (1.1) in our paper, $$ {u_{t}} = \operatorname{div} \bigl(\rho^{\alpha} \vert \nabla u \vert ^{p(x) - 2}\...