行星軌跡的加速度

Ask_Question · August 15, 2017

沿R方向的加速度為 $a_r = \frac{d^2r}{dt^2} - r\left( \frac{d\theta}{dt} \right)^2$

垂直R方向的加速度為 $a_{\theta} = \frac{1}{r}\frac{d}{dt}\left( r^2\frac{d\theta}{dt} \right)$

我用標座標R微分兩次後, 得到

${\mathbf {a}}=\left[{\frac {d^{2}r}{dt^{2}}}-r\left({\frac {d\theta }{dt}}\right)^{2}\right]{\mathbf {e}}_{r}+\left(2{\frac {dr}{dt}}{\frac {d\theta }{dt}}+r{\frac {d^{2}\theta }{dt^{2}}}\right){\mathbf {e}}_{\theta }.$

垂直分向的加速度不同.

請問垂直方向的加速度要怎樣求得?

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行星軌跡的加速度

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