本論文首先具體地以三個方法說明，擬似穩態馬赫反射流場之三震波解對正 存在有第一與第二個 解；對負sitaw 存在有第一、第二與第三個kai解，此三個方法係傳統擬似穩態馬赫反射流場之三震波理論、穩態馬赫反射流場轉換擬似穩態馬赫反射流場之十階多項式公式理論及擬似穩態馬赫反射流場之16階多項式公式理論，然後我們以此三種方法對4個不同的弱與強之擬似穩態馬赫反射流場入射震波馬赫數(Ms)作系列的(p-sita)震波極圖解，其中吾人主要變化入射震波角(phi1)值，自入射震波下游音速M1=1之波角到逆馬赫反射解域( i.e.有系統地變化sitaw)，有系統地討論多原子分子理想氣體(gamma=1.093)之擬似穩態馬赫反射流場三震波點路徑角(kai)非線性性質的多重解現象，並分析此多重kai解之alpha1、bata1 或bata2 之根性質屬性的問題。為了說明正sitaw (負sitaw )存在著第一與第二個(第一、第二與第三個)kai解的原因，吾人將擬似穩態馬赫反射流場三震波理論解固定Ms系列之計算結果表達於(phi1,sitaw)圖上，藉此(phi1,sitaw )圖說明global (整體)的正sitaw (負sitaw )之三震波理論多重解存在著第一與第二個(第一、第二與第三個)kai解的原理，最後應用吾人對於kai角多重解的了解，修正曾(2005)已定義擬似穩態馬赫反射流場之sitaw無法定義區，並確定其m值(震波極圖上大於D2點上之交點的數目)為3。

Three different methods are presented to theoretically calculate the first and second triple point trajectory angles (kai) of pseudo-steady Mach reflections (PMR) of positive reflecting wedge angles (sitaw) and calculate the first, second and third kai's of PMR of negative sitaw . They are (1) the traditional PMR three-shock theory solving 12 nonlinear algebraic conservation equations of the incident, reflected and Mach shocks and pressure and deflection slipstream compatibility equations along with a (usually normal straight) Mach stem/wall boundary condition; (2) the governing tenth degree polynomial algebraic equation of SMR transformed from PMR; (3) the 16th degree polynomial algebraic equation of PMR. Series of systematic examinations of global three-shock multiple kai solutions are carried out for four different incident shock Mach numbers (Ms) of perfect polyatomic gases (i.e.gamma=1.093) by primarily varying the incident shock angles (phi1) from the sonic forbidden condition downstream of the incident shock (i.e.M1=1) to phi1's of regions of inverse PMR using these three methods.alpha1、bata1 and bata2 root characteristics of multiply possible kai solutions of a given +sitaw or a given -sitaw are then investigated. In order to provide explanations for the existences of these multiply possible kai angles for a given PMR problem of sitaw, global three-shock theoretically calculated results, as phi1 systematically varying from M1=1 to the incident Mach angle condition for a given Ms are plotted on the (phi1,sitaw) plane, where three different patterns of global three-shock solution curves are identified for different ranges of Ms. Finally, based on the understanding of single or multiple kai solutions of a PMR problem of a given sitaw, we are able to correct the mistakenly classified undefined regime of the global three-shock PMR solutions of perfect polyatomic gases on the (Ms,sitaw) plane.

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