The Symbolic Form of Lagrange's Equation for a System in Periodic Motion and the Law of Conservation and Transformation of Vector Power for a System of Periodic Current Flowing in an Electrical Network

Abstract

The expression of complex instantaneous power and complex average power (vector power) of the periodic current is given. A special charactor of a hom- ogeneous function of second degree is explained. This is utilized to deduce the law of conservation and transformation of vector power in an electrical network from the symbo'ic form of Lagrange's equation. The formula which show the law of conservation of vector power for nth harmonic is Σ^k _p=1 [V_{p, n}, I_{p, n}]p+Σ^l _(pq) [E_pqmT_pqm]p=J(n)+j2nω{T(n)-U(n)}……(38) and the formula which may be made the basis for treating the frequency transformation by complex circuit constant is Σ^k _p=1 [V_{p, n}, I_{p, n}]p+Σ^l _(pq) [E_pqmT_pqm]p=J(n)+j2ω{T(n)-U(n)}……(77)
This formula is utilized to treat the problem of resisti e, inductive and condensive frequency transformation.