CAJ | 학술논문

推导柱坐标系及球坐标系下流体运动微分方程组通常采用的方法是根据矢量形式的运动微分方程式，利用物质导数的基本公式和正交曲线坐标系各基矢量的偏导数公式来进行，推导过程相当繁琐，尤其在教学过程中，在课堂内完成上述具体推导过程几乎是不可能的。为了寻找一种简捷的推导方法，本文依据基矢量物质导数的基本公式，计算得出了柱坐标系及球坐标系下的基矢量物质导数公式，并将它们分别应用于柱坐标系及球坐标系下的流体运动微分方程组的推导过程中。结果表明：如果将柱坐标系及球坐标系下基矢量的物质导数公式作为基本公式使用，则可以使上述坐标系下流体运动微分方程组的推导过程得到很大程度的简化。
추도주좌표계급구좌표계하류체운동미분방정조통상채용적방법시근거시량형식적운동미분방정식，이용물질도수적기본공식화정교곡선좌표계각기시량적편도수공식래진행，추도과정상당번쇄，우기재교학과정중，재과당내완성상술구체추도과정궤호시불가능적。위료심조일충간첩적추도방법，본문의거기시량물질도수적기본공식，계산득출료주좌표계급구좌표계하적기시량물질도수공식，병장타문분별응용우주좌표계급구좌표계하적류체운동미분방정조적추도과정중。결과표명：여과장주좌표계급구좌표계하기시량적물질도수공식작위기본공식사용，칙가이사상술좌표계하류체운동미분방정조적추도과정득도흔대정도적간화。
The methods usually used for derivation of fluid motion differential equations in cylindrical coordinates and spherical coordinates are based on the vector form of fluid motion differential equation, by using the basic formula of the material derivative and the partial derivative formulae of orthogonal curvilinear coordinates base vectors. The derivation process is very complex, especially in the teaching, it is almost impossible to complete the above specific derivation process in the classroom. In order to find a simple derivation method, based on the basic formulae of base vector material derivative, it is calculated that the base vector material derivative formulae in cylindrical coordinates and spherical coordinates, and they are applied to derivation process of fluid motion differential equations in cylindrical coordinates and spherical coordinates. The results show that:if the base vector material derivative formulae of cylindrical coordinates and spherical coordinates are used as basic formulae, then the derivation process of fluid motion differential equations in above coordinates will be simplified greatly.