ベレの方法
x → ( t + Δ t ) = x → ( t ) + v → ( t ) Δ t + a → ( t ) Δ t 2 2 + b → ( t ) Δ t 3 6 + O ( Δ t 4 ) x → ( t − Δ t ) = x → ( t ) − v → ( t ) Δ t + a → ( t ) Δ t 2 2 − b → ( t ) Δ t 3 6 + O ( Δ t 4 ) {\displaystyle {\begin{aligned}{\vec {x}}(t+\Delta t)&={\vec {x}}(t)+{\vec {v}}(t)\Delta t+{\frac {{\vec {a}}(t)\Delta t^{2}}{2}}+{\frac {{\vec {b}}(t)\Delta t^{3}}{6}}+{\mathcal {O}}(\Delta t^{4})\\{\vec {x}}(t-\Delta t)&={\vec {x}}(t)-{\vec {v}}(t)\Delta t+{\frac {{\vec {a}}(t)\Delta t^{2}}{2}}-{\frac {{\vec {b}}(t)\Delta t^{3}}{6}}+{\mathcal {O}}(\Delta t^{4})\end{aligned}}}
ここで、 x → {\displaystyle {\vec {x}}} は位置、 v → = x → ̇ {\displaystyle {\vec {v}}={\dot {\vec {x}}}} は速度、 a → = x → ̈ {\displaystyle {\vec {a}}={\ddot {\vec {x}}}} は加速度、 b → {\displaystyle {\vec {b}}} は躍度である。