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 February 11th, 2014, 01:22 AM #1 Newbie   Joined: Feb 2014 Posts: 1 Thanks: 0 Non-linear vectorial equation Hi everybody, I would like to solve the vectorial equation $\vec{v}= \vec{a} + b \, (\vec{x} \cdot \vec{v}) \, \vec{v} + c \, (\vec{x} \times \vec{v})^2 \, \vec{x}$ of unknown $\vec{v}$ where $\vec{a}$ and $\vec{x}$ are some vectors, $b$ and $c$ are some real numbers. I tried to decompose $\vec{v}$ as $\vec{v}= \vec{v_{\parallel}} + \vec{v_{\perp}}$ where $\vec{v_{\parallel}}$ and $\vec{v_{\perp}}$ are respectively colinear and orthogonal to $\vec{x}$. However, it doesn't seem to simplify the problem. Thank you in advance for your help.

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