Then, we change velocity coordinates from ( v x , v y , v z ) {\displaystyle (v_{x},v_{y},v_{z})} to the velocity parallel v | | ≡ v → ⋅ b ^ {\displaystyle v_{||}\equiv {\vec {v}}\cdot {\hat {b}}} , the magnetic moment μ ≡ m s v ⊥ 2 2 B {\displaystyle \mu \equiv {\frac {m_{s}v_{\perp }^{2}}{2B}}} , and the gyrophase angle φ {\displaystyle \varphi } . Here parallel and perpendicular are relative to b → ≡ B → / B {\displaystyle {\vec {b}}\equiv {\vec {B}}/B} , the direction of the magnetic field, and m s {\displaystyle m_{s}} is the mass of the particle. Now, we can average over the gyrophase angle at constant guiding center position, denoted by ⟨ … ⟩ φ {\displaystyle \left\langle \ldots \right\rangle _{\varphi }} , yielding the gyrokinetic equation.