Determination of Space-like Curves by Vector Differential Equations in Minkowski Space E$_{1}^{3}$

In this paper, position vectors of space-like curves in Minkowski space E$^3_1$ according to standard frame are investigated. First, it is proven that position vector of every space-like curve with space-like or time-like principal normal satisfies a vector differential equation of fourth order. By means of a special solution, we obtain position vector of a space-like $W-$curve (helix, i.e.) with space-like or time-like principal normal according to standard frame of E$^3_1$. Additionally, by applying same method to space-like curves with null principal normal, we obtain position vector of space-like $W-$curves with null principal normal according to standard frame.