MHB Is There a Solution for 6 Degree of Freedom Solid Body Movement Equations?

[Anton1]

Hi, I ended up with the following 3 equations that relate to solving 6 degree of freedom solid body movement. The equations relate to rotations around the x, y and z axis (which is far more complicated than translations). Is there anybody that knows the solution or can figure it out (i am just an engineer and have not done proper maths for about 30 years!)?
Thanks
Anton

k, m and n are constants:


View attachment 5352

 

[Ackbach]

The following Mathematica command solves the system, but the solution is horrendous:

Solve[{x==k1+k2 z y-k3 y-k4 z,y==m1 +m2 z x -m3 x-m4 z,z==n1+n2 x y-n3 y-n4 x},{x,y,z}]

Do you know the exact values of the constants? If so, I think the solution would be much simpler in form.

 

[Anton1]

Thanks, that was so quick! Can you provide the solution please (I really don't mind if it is horrendous!?

I do know the exact values of the constants but I think it unlikely that this will simplify the form...

I attach the full background, I'm sure solutions must exists for this but after much searching I still have not found them.

 

[Ackbach]

Unfortunately, I don't have a full copy of Mathematica at the moment. The best I can do is the Wolfram Development Platform, which is not giving me enough server time to display the entire thing. Stay tuned. I may be able to get a full copy of Mathematica through my research connection.

 

[topsquark]

Unfortunately, I don't have a full copy of Mathematica at the moment. The best I can do is the Wolfram Development Platform, which is not giving me enough server time to display the entire thing. Stay tuned. I may be able to get a full copy of Mathematica through my research connection.

I have a full copy of Mathematica. It doesn't help, the system is fugly.

-Dan

 

[Anton1]

I have a full copy of Mathematica. It doesn't help, the system is fugly.

-Dan

Thanks guys, even though it may not be the result I was hoping for at least now I know that apparently it does not have an explicit solution. Appreciate the answers.