I am trying to solve the following equation in Excel for over a year now but the size of it is absolutely massive. This equation is used in a spreadsheet that I am making to model the suspension of my Jeep. I have no idea how to enter all of this information into Mathematica. Any help at all would be greatly appreciated.
I want to solve the following equation in terms of y and B and solve for B based on a given y:
y=B+RearCoupler101*(B-D) -SQRT(RearCoupler102^2-RearCoupler101^2)*(C-A);
where:
C = RearLowerFrameX - SQRT(RearLowerDistance^2-(D-RearLowerFrameY)^2);
A = RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2);
D = ( (B+RearLowerFrameY) * (A-RearLowerFrameX)^2 +
(RearLowerDistance^2-RearAxleDistance^2-RearLowerFrameY^2+B^2) * (B-RearLowerFrameY) +(A-RearLowerFrameX) * SQRT(2* (RearLowerDistance^2+RearAxleDistance^2) * ((A-RearLowerFrameX)^2+(B-RearLowerFrameY)^2)-((A-RearLowerFrameX)^2 +(B-RearLowerFrameY)^2)^2-(RearLowerDistance^2-RearAxleDistance^2)^2))/(2*(A-RearLowerFrameX)^2+2*(B-RearLowerFrameY)^2);
RearCoupler101 = (RearLowertoAxleDistance^2 - RearUppertoAxleDistance^2 - RearAxleDistance^2)/(2*RearAxleDistance^2);
RearCoupler102 = RearUppertoAxleDistance/RearAxleDistance;
RearUpperDistance = SQRT((RearUpperFrameX-RearUpperAxleX)^2+(RearUpperFrameY-RearUpperAxleY)^2);
RearLowerDistance = SQRT((RearLowerFrameX-RearLowerAxleX)^2+(RearLowerFrameY-RearLowerAxleY)^2);
Rear Axle Distance = SQRT((RearUpperAxleX-RearLowerAxleX)^2+(RearUpperAxleY-RearLowerAxleY)^2);
RearUppertoAxleDistance = SQRT((RearUpperAxleX-RearTireCenterX)^2+(RearUpperAxleY-RearTireCenterY)^2);
RearLowertoAxleDistance = SQRT((RearLowerAxleX-RearTireCenterX)^2+(RearLowerAxleY-RearTireCenterY)^2);
RearUpperFrameX = 31.625;
RearUpperFrameY = 27;
RearUpperAxleX = 3.375;
RearUpperAxleY = 30.125;
RearLowerFrameX = 37.875;
RearLowerFrameY = 23.25;
RearLowerAxleX = 3.75;
RearLowerAxleY = 20.375;
RearTireCenterX = 0;
RearTireCenterY = 20.5;
When I combine all of the pieces together I can create a single equation that has only y and B but it has three square roots and I am about half way through solving it by hand, but hopefully some genius here can solve it ten minutes. I would like to see how it is entered into Mathematica so I can possibly try an even more complicated formula for the articulation of the axles. Thanks in advance for any help you guys can provide.
Here is the full equation:
0 = -y + B -RearCoupler101 * (B- ( (B+RearLowerFrameY) * ( (RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX)^2 +
(RearLowerDistance^2-RearAxleDistance^2-RearLowerFrameY^2+B^2) * (B-RearLowerFrameY) +( (RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX) * SQRT(2 * (RearLowerDistance^2+RearAxleDistance^2) * (( (RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX)^2+(B-RearLowerFrameY)^2)-(( (RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX)^2 +(B-RearLowerFrameY)^2)^2-(RearLowerDistance^2-RearAxleDistance^2)^2))/(2 * ( (RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX)^2+2 * (B-RearLowerFrameY)^2))+SQRT(RearCoupler102^2-RearCoupler101^2) * (RearLowerFrameX - SQRT(RearLowerDistance^2-( ( (B+RearLowerFrameY) * ((RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX)^2 +
(RearLowerDistance^2-RearAxleDistance^2-RearLowerFrameY^2+B^2) * (B-RearLowerFrameY) +((RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX) * SQRT(2 * (RearLowerDistance^2+RearAxleDistance^2) * (((RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX)^2+(B-RearLowerFrameY)^2)-(((RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX)^2 +(B-RearLowerFrameY)^2)^2-(RearLowerDistance^2-RearAxleDistance^2)^2))/(2 * ((RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2))-RearLowerFrameX)^2+2 * (B-RearLowerFrameY)^2)-RearLowerFrameY)^2)-(RearUpperFrameX - SQRT(RearUpperDistance^2-(B-RearUpperFrameY)^2)));
Thank you all for the responses. Here is a graphical representation of what I am trying to come up with. In this graph I am changing the RearUpperAxleY coordinate and the rest of the coordinates are calculated.
https://www.geogebra.org/m/wxnwM45t
What I am looking for is to be able to change the RearTireCenterY coordinate and calculate the rest of the coordinates. Someone at Geogebra used a locus to approximate what I am trying to do, but I need an exact calculation. Perhaps I am trying to solve the equation the wrong way. I don't care what order the coordinates are solved, just so long as I can calculate all the coordinates after changing RearTireCenterY.
https://www.geogebra.org/m/dDRQwtqE
What I really need to know is the equation, but also how the equation was created. I have several other formulas after this one that can be solved in the same manner, I just to figure out how to solve it the first time.
D
is a protected symbol in Mathematica. You'll have to change it to something else. It's always a good idea to use lower case letters for your variables and functions. $\endgroup$