Numerical Solution of Axisymmetrical Problems, with Applications to Electrostatics and Torsion

摘要: Numerical methods are given for solution of axisymmetrical problems involving the partial differential equation ∂2ψ∂z2+∂2ψ∂ρ2+Kρ∂ψ∂ρ=0, where ρ is radial coordinate and z parallel to axis. The various values K which occur in physical situations discussed, common iteration handling these given. For Laplace's equation, = 1. Stoke's stream function, − 1, but it pointed out that numerical work a new called flow‐disturbance having 3, more tractable. Similarly function with 5, stress‐concentration much easier compute than usual stress (K 3) case torsion circular shaft varying diameter. illustrated by computation equipotentials an electron lens, complete stresses strains particular grooved under torsion.