needs to solve system of 4 eqns, 4 unknowns
needs to solve system of 4 eqns, 4 unknowns
(OP)
Hello All,
I what what I thought (once again!) was a fairly straight-forward problem to solve, but I can't quite seem to get there. I have 4 eqns, 4 unknowns. Equations are along the lines of:
sqrt(x^2+y^2) + z + sqrt((val1-x)^2 + (y-val2)) + Const1 = 0
sqrt(x^2+y^2) + z + Const2 = 0
sqrt(x^2+y^2) + z + 3*sqrt((x-val3)^2 + (y-val3)) + Const3 = 0
sqrt(x^2+y^2) + z + 2*sqrt((val4-x)^2 + (y-val2)) + Const4 = 0
In each case, "valn" is known, as is "Constn." "Constn" may consist of 1 or more values, here combined for simplicity.
I've tried a number of methods...from transforming the equations into other forms, combining equations in several ways, etc. Does anyone have a sound method for solving this type of problem?
Any help GREATLY appreciated. Thanks!
I what what I thought (once again!) was a fairly straight-forward problem to solve, but I can't quite seem to get there. I have 4 eqns, 4 unknowns. Equations are along the lines of:
sqrt(x^2+y^2) + z + sqrt((val1-x)^2 + (y-val2)) + Const1 = 0
sqrt(x^2+y^2) + z + Const2 = 0
sqrt(x^2+y^2) + z + 3*sqrt((x-val3)^2 + (y-val3)) + Const3 = 0
sqrt(x^2+y^2) + z + 2*sqrt((val4-x)^2 + (y-val2)) + Const4 = 0
In each case, "valn" is known, as is "Constn." "Constn" may consist of 1 or more values, here combined for simplicity.
I've tried a number of methods...from transforming the equations into other forms, combining equations in several ways, etc. Does anyone have a sound method for solving this type of problem?
Any help GREATLY appreciated. Thanks!





RE: needs to solve system of 4 eqns, 4 unknowns
Fe
RE: needs to solve system of 4 eqns, 4 unknowns
If you are 100% certain they are correct relations then a numerical solution may be possible. This is a real 'may' though.
Fe
RE: needs to solve system of 4 eqns, 4 unknowns
My bad, I mis-entered the equations in first post
sqrt(x^2+y^2) + t + sqrt((val1-x)^2 + (y-val2)) + Const1 = 0
sqrt(x^2+y^2) + t + Const2 = 0
sqrt(x^2+y^2) + t + 3*sqrt((x-val3)^2 + (z-val3)) + Const3 = 0
sqrt(x^2+y^2) + t + 2*sqrt((val4-y)^2 + (z-val2)) + Const4 = 0
x, y, z, and t are unknown. All other conditions same as before. Also keep in mind these are not my exact equations. val1, val2, val3, val4 are known.
RE: needs to solve system of 4 eqns, 4 unknowns
TTFN
FAQ731-376: Eng-Tips.com Forum Policies
Chinese prisoner wins Nobel Peace Prize
RE: needs to solve system of 4 eqns, 4 unknowns
See the attached. Looks like you have 8 solutions to those equations numerically.
Fe
RE: needs to solve system of 4 eqns, 4 unknowns
RE: needs to solve system of 4 eqns, 4 unknowns
-Const2 + sqrt((val1-x)^2 + (y-val2)) + Const1 = 0
-Const2 + 3*sqrt((x-val3)^2 + (z-val3)) + Const3 = 0
-Const2 + 2*sqrt((val4-y)^2 + (z-val2)) + Const4 = 0
reoorg 1 to give y in terms of x, chuck that into 3, reorg that to give x in terms of z, chuck that into 2 for a nasty polynomial in z.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: needs to solve system of 4 eqns, 4 unknowns
sqrt((val1-x)^2 + (y-val2)) = Const1'
sqrt((x-val3)^2 + (z-val3)) = Const3'
sqrt((val4-y)^2 + (z-val2)) = Const4'
square all eq
(val1-x)^2 + (y-val2) = Const1"
(x-val3)^2 + (z-val3) = Const3"
(val4-y)^2 + (z-val2) = Const4"
eliminate z terms from (2) & (3)
now two eqn left so sub for x terms in (1)
plot eqn left standing against y and back sub the root(s)
for x & z
rainy day fun for op