Maple
姓名：xxx 学号：xxxxxx 班级：xxx
作业
Maple例题；
1．y?1x3?1 ，求
dy。 dx> restart:
> y:=1/(sqrt(x^3)+1): > diff(y,x);
3?2
x2(x???1)32x3
2. 连续梁的支座如图所示。设q?10kNm，试用Maple语言编写求所有支座约束力的程序。
题2图 > restart:
> eq1:=-q*2*l*l+FD*2*l=0: > eq2:=FCx=0:
> eq3:=FCy+FD-q*2*l=0: > eq4:=FAx=0:
> eq5:=-q*4*l*2*l+FB*l+FD*4*l=0: > eq6:=FAy+FB+FD-q*4*l=0:
> SOL1:=solve({eq1,eq2,eq3,eq4,eq5,eq6},{FAx,FAy,FB,FCx,FCy,FD}): > FAx:=subs(SOL1,FAx): > FAy:=subs(SOL1,FAy): > FB:=subs(SOL1,FB): > FCx:=subs(SOL1,FCx): > FCy:=subs(SOL1,FCy): > FD:=subs(SOL1,FD): > q:=10e3: l:=1: > FAx:=evalf(FAx,4);
FAx := 0.
> FAy:=evalf(FAy,4); > FB:=evalf(FB,4); > FCx:=evalf(FCx,4);
FAy := -10000. FB := 40000.
FCx := 0.
> FCy:=evalf(FCy,4);
FCy := 10000.
> FD:=evalf(FD,4);
FD := 10000.
3. 图示曲线规尺的杆长OA?AB?200mm，而CD?DE?AC?AE?50mm。如OA杆以等角速度???5（1）求尺上D点的运动方程。 （2）求D点轨迹，并绘图。
rads绕O轴转动，并且当运动开始时，角??0?。
题3图
> restart:
> OA:=l: AB:=l: CD:=l/4: DE:=l/4: AC:=l/4: AE:=l/4: > phi:=omega*t: > x:=OA*cos(phi):
> y:=(OA-2*AC)*sin(phi): > eq:=X^2/l^2+Y^2/(l/2)^2=1:
> x:=evalf(subs(l=0.2,omega=Pi/5,x),4);
x := .2cos(.6284t)
> y:=evalf(subs(l=0.2,omega=Pi/5,y),4);
y := .1000sin(.6284t)
> eq:=evalf(subs(l=0.2,eq),4);
eq := 25.00X2???100.0Y2???1.
> with(plots):
> implicitplot({eq},X=-0.2..2,Y=-0.1..0.1);
题3图
?341???4.已知A?075， ????119??> restart:
> with(linalg):
> A:=matrix(3,3,[3,4,1,0,7,5,1,1,9]);
?3?A := ??0??1?> det(A);
4711??5???9??
187
> transpose(A);
?3??4???1?> inverse(A);
0751??1???9??
?58??187??5???187???-7??187?> evalf(eigenvals(A));
-3518726187118713??187??-15??
?187???21??187??11.,4.???1.I,4.???1.I
?x5. 试由Maple基本行运算来求矩阵A???2x的指令验证所求得的结果。 > restart:
> with(linalg):
x2??的逆矩阵，并以直接求A逆矩阵x?1??x> A:=matrix(2,2,[[x,x^2],[2*x,x+1]]);A := ??2x?
x2?? x???1??> B:=matrix(2,4,[[x,x^2,1,0],[2*x,x+1,0,1]]);
x21?xB := ??2xx???10?x2?x> B1:=addrow(B,1,2,-2);B1 := ???0?2x2???x???1??1x??> B2:=mulrow(B1,1,1/x);B2 := ???0?2x2???x???1?> B3:=mulrow(B2,2,1/(-2*x^2+x+1));
0?? 1??10?? ?-21??10??? x??-21?????? ?1??2?2x???x???1??0?1??B3 := ????0??> B4:=addrow(B3,2,1,-x);
x11x2??2x2???x???12x1x??????22x?2x???x???1?2x???x???1??
??21?1??22?2x???x???1?2x???x???1??x???1x?????22?x(2x???x???1)?2x???x???1?? > inverse(A); ????21?????22?2x???x???1?2x???x???1??6. 图示三铰拱，本身重量不计。设P?30kN，Q?20kN，试用Maple语言编写求
?1??B4 := ????0???0所有支座约束力的程序。
题6图
> restart:
> eq1:=FAx+FBx=0: > eq2:=FAy+FBy-P-Q=0:
> eq3:=P*(a[2]+a[3]+a[4])+Q*a[4]-FAx*(h[2]-h[1])-FAy*(a[1]+a[2]+a[3]+a[4])=0: > eq4:=FAx+FCx=0: > eq5:=FAy+FCy-P=0:
> eq6:=FAx*h[1]-FAy*(a[1]+a[2])+P*a[2]=0:
> SOL1:=solve({eq1,eq2,eq3,eq4,eq5,eq6},