[已解决] 6元一次参数方程求多解

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Mr.yan123 发表于 2022-10-8 09:57:31
代码如下
syms theta1 theta3 theta4 theta5 theta6  D X Y Z M N
eqn = [X*cos(theta1) + Y*sin(theta1)==M*cos(theta3)*cos(theta4) + N*cos(theta6)*(sin(theta3)*sin(theta5) + cos(theta3)*cos(theta4)*cos(theta5)) + N*cos(theta3)*sin(theta4)*sin(theta6) ,
       -Z== M*sin(theta4) - N*cos(theta4)*sin(theta6) + N*cos(theta5)*cos(theta6)*sin(theta4),
       Y*cos(theta1) - X*sin(theta1)==D - M*cos(theta4)*sin(theta3) + N*cos(theta6)*(cos(theta3)*sin(theta5) - cos(theta4)*cos(theta5)*sin(theta3)) - N*sin(theta3)*sin(theta4)*sin(theta6),
       D*sin(theta3) + X*cos(theta1 - theta3) + Y*sin(theta1 - theta3)==M*cos(theta4) + N*sin(theta4)*sin(theta6) + N*cos(theta4)*cos(theta5)*cos(theta6),
       Y*cos(theta1 - theta3) - D*cos(theta3) - X*sin(theta1 - theta3)== N*cos(theta6)*sin(theta5),
       D*cos(theta4)*sin(theta3) - Z*sin(theta4) - M + X*cos(theta1)*cos(theta3)*cos(theta4) - Y*cos(theta1)*cos(theta4)*sin(theta3) + Y*cos(theta3)*cos(theta4)*sin(theta1) + X*cos(theta4)*sin(theta1)*sin(theta3)==N*cos(theta5)*cos(theta6),
       N*sin(theta6)== Z*cos(theta4) + D*sin(theta3)*sin(theta4) + X*cos(theta1)*cos(theta3)*sin(theta4) - Y*cos(theta1)*sin(theta3)*sin(theta4) + Y*cos(theta3)*sin(theta1)*sin(theta4) + X*sin(theta1)*sin(theta3)*sin(theta4),
       N*cos(theta6)==D*cos(theta4)*cos(theta5)*sin(theta3) - D*cos(theta3)*sin(theta5) - Z*cos(theta5)*sin(theta4) - M*cos(theta5) + Y*cos(theta1)*cos(theta3)*sin(theta5) + X*cos(theta1)*sin(theta3)*sin(theta5) - X*cos(theta3)*sin(theta1)*sin(theta5) + Y*sin(theta1)*sin(theta3)*sin(theta5) + X*cos(theta1)*cos(theta3)*cos(theta4)*cos(theta5) - Y*cos(theta1)*cos(theta4)*cos(theta5)*sin(theta3) + Y*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta1) + X*cos(theta4)*cos(theta5)*sin(theta1)*sin(theta3),
       D*cos(theta3)*cos(theta5) - M*sin(theta5) - Z*sin(theta4)*sin(theta5) - Y*cos(theta1)*cos(theta3)*cos(theta5) + D*cos(theta4)*sin(theta3)*sin(theta5) - X*cos(theta1)*cos(theta5)*sin(theta3) + X*cos(theta3)*cos(theta5)*sin(theta1) - Y*cos(theta5)*sin(theta1)*sin(theta3) + X*cos(theta1)*cos(theta3)*cos(theta4)*sin(theta5) - Y*cos(theta1)*cos(theta4)*sin(theta3)*sin(theta5) + Y*cos(theta3)*cos(theta4)*sin(theta1)*sin(theta5) + X*cos(theta4)*sin(theta1)*sin(theta3)*sin(theta5)==0
       ];
answ = solve(eqn, [theta1, theta3, theta4, theta5, theta6,  D])



这样写怎么算一上午不出来结果,帮帮老弟吧

最佳答案


cbcbcbcb 发表于 2022-10-8 10:43:38
Mr.yan123 发表于 2022-10-8 10:35
老哥,就是想求带参数的解,M,N是已知的,能否用xyz表示某个theta角,其他的theta用这个角表示呢 ...

老弟,看一下这个帖子吧,对你应该有启发的,基本上是求不出来解析解的,链接如下:
https://www.ilovematlab.cn/forum ... read&tid=617669

4 条回复


shihe 发表于 2022-10-8 10:25:05
该方程组应该是不存在解析解吧。给出D X Y Z M N的具体数值,用fsolve或vpasolve求数值解

Mr.yan123 发表于 2022-10-8 10:35:55
shihe 发表于 2022-10-8 10:25
该方程组应该是不存在解析解吧。给出D X Y Z M N的具体数值,用fsolve或vpasolve求数值解 ...

老哥,就是想求带参数的解,M,N是已知的,能否用xyz表示某个theta角,其他的theta用这个角表示呢

cbcbcbcb 发表于 2022-10-8 10:43:38
Mr.yan123 发表于 2022-10-8 10:35
老哥,就是想求带参数的解,M,N是已知的,能否用xyz表示某个theta角,其他的theta用这个角表示呢 ...

老弟,看一下这个帖子吧,对你应该有启发的,基本上是求不出来解析解的,链接如下:
https://www.ilovematlab.cn/forum ... read&tid=617669
回复此楼

Mr.yan123 发表于 2022-10-8 10:44:25
cbcbcbcb 发表于 2022-10-8 10:43
老弟,看一下这个帖子吧,对你应该有启发的,基本上是求不出来解析解的,链接如下:
https://www.ilovema ...

好的老哥
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