[SOLVED] Equation system to solve

**crapmathematician** · May 5th 2010, 02:18 PM

Hi,

Got this equation system to solve, and its just not going anywhere to me, keep banging a dead end... Hope you guys can help. The unknowns are d1 and d2, the rest is assumed as known.

Any help appreciated!

THNX!

**Anonymous1** · May 5th 2010, 03:15 PM

Originally Posted by crapmathematician

Hi,

Got this equation system to solve, and its just not going anywhere to me, keep banging a dead end... Hope you guys can help. The unknowns are d1 and d2, the rest is assumed as known.

Any help appreciated!

THNX!

$x_1 - d_1 \sin x_1= x_2 + d_2 \cos x_2 \rightarrow(1)$

$y_1 - d_1 \cos x_1= y_2 + d_2 \sin x_2 \rightarrow(2)$

Rearrange $(1): x_1 - x_2 - d_2 \cos x_2 = d_1 \sin x_1$

$\Rightarrow d_1 = \frac{x_1 - x_2 - d_2 \cos x_2}{\sin x_1} \rightarrow(3)$

Now sub $(3)$ into $(2)$ and solve for $d_2.$

Then, plug the $d_2$ you found into $(1)$ to find $d_1.$

**crapmathematician** · May 6th 2010, 10:45 AM

Originally Posted by Anonymous1

$x_1 - d_1 \sin x_1= x_2 + d_2 \cos x_2 \rightarrow(1)$

$y_1 - d_1 \cos x_1= y_2 + d_2 \sin x_2 \rightarrow(2)$

Rearrange $(1): x_1 - x_2 - d_2 \cos x_2 = d_1 \sin x_1$

$\Rightarrow d_1 = \frac{x_1 - x_2 - d_2 \cos x_2}{\sin x_1} \rightarrow(3)$

Now sub $(3)$ into $(2)$ and solve for $d_2.$

Then, plug the $d_2$ you found into $(1)$ to find $d_1.$

That's where the problem is! When I put (3) into (2) to solve for $d_1$ I get a beast which looks like this:

and I have no clue how to make it tidy to solve for $d_1$

**Anonymous1** · May 6th 2010, 11:03 AM

$\frac{x_1 \cos x_1 - x_2 \cos x_1 - d_2 \cos x_1 \cos x_2}{\sin x_1} = y_2 - y_1 + d_2 \sin x_2$

$\implies x_1 \cos x_1 - x_2 \cos x_1 - d_2 \cos x_1 \cos x_2 = y_2 \sin x_1 - y_1 \sin x_1 + d_2 \sin x_2 \sin x_1$

$\implies x_1 \cos x_1 - x_2 \cos x_1 - y_2 \sin x_1 + y_1 \sin x_1 = d_2 \sin x_2 \sin x_1 + d_2 \cos x_1 \cos x_2$

$\implies x_1 \cos x_1 - x_2 \cos x_1 - y_2\sin x_1 + y_1 \sin x_1 = d_2 (\sin x_2 \sin x_1 + \cos x_1 \cos x_2 )$

$\implies d_2 = \frac{x_1 \cos x_1 - x_2 \cos x_1 - y_2 \sin x_1 + y_1 \sin x_1}{\sin x_2 \sin x_1 + \cos x_1 \cos x_2}.$

Yeah it's ugly, but I'm not sure I see the issue...?

**crapmathematician** · May 13th 2010, 10:39 PM

Change of situation!!!

If I assume that I know d1 and d2 but do not know alpha1 and alpha2 instead. From equation 1 I have expressed sina1 which results as (x1-x2-d2*cosa2)/d1. How do I change this in order to be able to substitute for cosa1 in equation 2? Or is there another way to solve it?

Thread: [SOLVED] Equation system to solve

LinkBack

Thread Tools

Display

[SOLVED] Equation system to solve

Similar Math Help Forum Discussions

solve an equation system!!!

Solve an equation system

[SOLVED] using matrices to solve for a system of equations using gaussian elimination

Solve the equation system

Use system of equation to solve

Search Tags