更多信息和选项 范例 基本范例(3) In[1]:= Laplacian of a function in Cartesian coordinates: In[2]:= Out[2]= In[1]:= Verify that a function is harmonic: In[2]:= Out[2]= In[1]:= Expression for the Laplacian in cylindrical coordinates: In[2]:= Out[2]=...
Eqs.ofmotionincylindricalcoordinates Eq.ofMotion Conservationofangularmomentum z-componentJzifaxisymmetric Thecomponentofangularmomentumaboutthez-axisisconserved. If(R,z)hasnodependenceonthentheazimuthalangularmomentumisconserved orbecausez-componentofthetorquerF=0.(Showit) ...
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 , ...
When finite difference (FD) is applied to higher order partial derivatives, the derivation or computation of the expression is easily maneuverable for rectangular coordinates. But cylindrical counterparts suffer from expressional as well as computational complexity. Even with the rectangular derivatives, ...
更多信息和选项 范例 基本范例(3) In[1]:= Laplacian of a function in Cartesian coordinates: In[2]:= Out[2]= In[1]:= Verify that a function is harmonic: In[2]:= Out[2]= In[1]:= Expression for the Laplacian in cylindrical coordinates: In[2]:= Out[2]=...
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^...