扭面方程和箱變坐標(biāo)系簡介(英文)_曹玉聘(編輯修改稿)
2024-09-19 00:45 本頁面
【文章內(nèi)容簡介】 t seeking for screwy surface equation [shown by (1) formula]. The basic method was: first set up a certain norm coordinate unit (such as coordinate unit on coordinate axis), then multiply a properly changed certain function of coordinate unit (could be called coordinate coefficient, its seeking method could be seen below). Then, mathematic characteristics of various sides could be seen from Table 2.The above were initial train of thoughts for solution to the problems of screwy surfaces. Simplified table of mathematic characteristics of various sides of linear positive box body Table 2Side High distanceWide distanceSide high distance arithmetic formulaRemarksHorizontal 1H11,H12LX1HX1=HX1(X)=AHX1+BHX1XAHX1=H11, BHX1=(H12H11)/LX1Horizontal 2H21,H22LX2≠LX1HX2=HX2(X)=AHX2+BHX2XAHX2=H21, BHX2=(H22H21)/LX1Vertical 1H11,H21LY1HY1=HY1(Y)=AHY1+BHY1YAHY1=H11, BHY1=(H21H11)/LY1Vertical 2H12,H22LY2≠LY1HY2=HY2(Y)=AHY2+BHY2YAHY2=H12, BHY2=(H22H12)/LY1 Nonlinear screwy surface equation: Chart 4 showed a nonlinear straight box body (could also be other nonlinear positive box body), H11H12H22H21 were a nonlinear screwy surfaces, changes on various sides took secondary parabola as example (such as Table 3, could also be other nonlinear change). Try to seek for that screwy surfaces equationChart 4 Nonlinear box bodySimplified table of mathematic characteristics of various sides of nonlinear positive box body Table 3SideHigh distanceWide distancePositive thickness equationRemarks Horizontal 1H11,H12LX1HX1=HX1(X)=AHX1+BHX1X+CHX1X2Various equations could adopt parabola method to seek, out of which, X, Y were coordinate value or coordinate unit amount on corresponding coordinate axis.Horizontal 2H21,H22LX2≠LX1HX2=HX2(X)=AHX2+BHX2X+CHX2X2Vertical 1H11,H21LY1HY1=HY1(Y)=AHY1+BHY1Y+CHY1Y2Vertical 2H12,H22LY2≠LY1HY2=HY2(Y)=AHY2+BHY2Y+CHY2Y2It was difficult for such equation to directly seek, however, if vertical and horizontal oneway nonlinear change (HX2Y,HY2X) were sought according to the above train of thoughts and method, then deduct a twoway linear change(HXY), the problem would be solved without any difficulty. Its ordinary seeking method was shown as follows: H(X,Y)=HX2Y+HY2XHXY， (2)Among HX2Y(X,Y)=HX1+(HX2HX1)Y/LY1，HY2X(X,Y)=HY1+(HY2HY1)X/LX1，HXY(X,Y) was shown as formula(1)Insert the above 3 formulas into formula (2), upon pletion, could gain screwy surfaces equation as: H(X,Y)=AH+BHxX+BHyY+CHxxX2+CHxyXY+CHyyY2+DHxxyX2Y+DHxyyXY2 () Formula，AH=H11，BHx=BHX1，BHy=BHY1，CHxx=CHX1，CHxy=(BHX2BHX1)/LY1+(BHY2BHY1)/LX1(H22H21 H12+H11)/LX1/LY1，CHyy=CHY1，DHxxy=(CHX2CHX1)/LY1，DHxyy=(CHY2CHY1)/LX1。The above seeking method took lead in realizing various screwy surface equation accurate expression and the relevant operations.2. A brief introduction to box transformation coordinate systemApply the above seeking train of thoughts and method to conventional rectangular coordinate system, and gain universal box transformation coordinate system, the following is a brief introduction: Box transformation coordinate system’s mathematic agreement Chart 5 Linear box transformation coordinate systemKX(Y)=1+KXBY,KY(X)=1+KYBX,KH(X,Y)=1+KHxX+KHyY+KHxyXYBox transformation coordinate system could take a certain standard positive box body (real line in Chart 5) as norm or primary type(called base box body), and was made through corresponding net form cutting according to geometric proportion(broken line in Chart 5), out of which, coordinate net corresponding to base coordinate net was called norm net. The box transformation coordinate system also had plane (box surfaces) and space (box body) coordinate systems. In box transformation coordinate system, base box body’s length, width and height on the 3 coordinate axes were respectively called
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