本論文首先應用穩態馬赫反射流場運動方程式及斜震波關係式，推導出理想氣體穩態馬赫反射流場之反射震波下游之音速條件與反射震波之強弱分界條件之曲線解公式，並應用該曲線解公式來推導反射震波俱音速性質於Mach angle條件及反射震波俱強弱分界性質於Mach angle條件之 公式。隨後本文由石(2004)論文中加入前後分界、機械平衡、M2=1及強弱分界條件，然後有系統地探討三原子分子理想氣體 (r=1.2857 ) 穩態馬赫反射參震波理論多重解之交點及其對應之壓力-轉折角震波極圖解，並建構出此三原子分子理想氣體穩態馬赫反射流場三震波十階多項式理論解於(Mo,q1)平面上之解域圖，其中M0為入射震波上游流場馬赫數，M1為入射震波下游流場馬赫數，M2為入射震波下游流場馬赫數，q1為入射震波下游流場轉折角。同時証明在(Mo,q1)平面上之解域圖上，M2=1曲線、WuestI曲線、前向音速曲線、前向強弱曲線、前後分界曲線並無相交。最後吾人針對WuestII曲線、後向音速曲線、後向強弱曲線、機械平衡曲線，推導它們之間的交點解公式 ，並將計算的結果標示於 平面上之解域圖上。

ABSTRACT
In this thesis, we apply the equations of motion of steady Mach reflections and the oblique shock theory to derive polynomial expressions of the forms of f(r,Mo,P1) of downstream sonic and strong/weak separating conditions of reflected shocks of perfect-gas steady Mach reflections. We then obtain polynomial expressions of the forms of f(r,M0) for the limiting Mach angle condition of the above two expressions. We then add boundaries delineated forward/backward facing reflected shock, Mechanical equilibrium, M2=1 and reflected shock strong/weak separating conditions on the (M0,q1) map of shih(2004). This is followed by systematically investigating multiply possible three shock theoretical solutions of steady Mach reflections in perfect triatomic gases. Pressure-deflection shock polar solutions are used to help illustrate different solution behaviors of these theoretical three-shock solutions. M0 is flow Mach no. upstream of incident shock, M1 is flow Mach no. downstream of incident shock, M2 is flow Mach no. downstream of reflected shock,q1 is flow deflection downstream of incident shock. We show that solution curves of M1=1 , WuestI, reflected shock forward-facing sonic, reflected shock forward-strong/weak separating, and reflected shock forward/backward facing conditions are not intersected. On the other formed, polynomial expressions of intersected point between solution curves of WuestII, reflected shock backward-facing sonic, reflected shock backward-strong/weak separating, Mechanical equilibrium are derived and computed results are marked on the (M0,q1) theoretical solution map of perfect triatomic gas steady Mach reflection.

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