セツゾクケイ ノ ジユウ シンドウ (シュトシテ タカハシ ノ ホウホウ ト コユウ カンスウ ニツイテ)

There are many arbitrary constants in the general solutions of the equations for the free vibrations of a frame work consisting of many bars. We have been obliged to make great efforts to determine these constants from the boundary conditions and the equations of continuity at the rigidly jointed corners and then to obtain the frequency equation of this system. Professor Shin Takahashi found in 1961 an available method in which we would carry out easily a process to decide the values of these constants and to find the frequency equation. This method is called |Lagrangian-minimizing-method| or |Takahashi\u27s method|. In this paper we will exhibit the dynamical meaning of the Takahashi\u27s method and the general properties of the normal functions for the free vibrations by means of the calculus of variation