# Help or hint with solving system of polynomial equations.

After few years my math skills got a bit rusty and I don't seem to remember how to classify and solve a problem I'm lookin at.

I have four equations and four variables:

$a_xt^2 +At + B=0$

$a_yt^2 +Ct + D=0$

$a_zt^2 +Et + F=0$

$a_x^2 + a_y^2 + a_z^2 = G$

The variables are: $a_x,a_y,a_z,t$ and $t >0$

In short it's an equation that calculates acceleration vector in certain motion during time t. I know the magnitude of the acceleration vector but I want to know how to distribute the components and how long will this motion take. If time t is known the problem becomes trivial. The biggest challenge comes from fact that a is time dependent, $a(t)$.

Could anyone point me in a direction? What problem I'm looking at and whether it's solvable analytically ? If not what numerical method I should use?

At least a gentle poke in the right direction would be much appreciated.

Many thanks

• Thanks, but I can't see how it will help me here? The ax,ay,az are variables not constants, t is squared. It's not a linear equation so I don't see how I can use this method? May 9, 2016 at 14:06