Acceleration in Spherical Coordinates 2

Part 1

When using spherical coordinates for space curvilinear motion the expression for acceleration in the direction of increasing \(\theta\) is

Answer Section

• \(a_{\theta} = \ddot{R} - R\dot{\phi}^2-R\dot{\theta}^2\:cos^2\phi\)

• \(a_{\theta} = \frac{cos\phi}{R}\frac{d}{dt}(R^2\dot{\theta})-2R\dot{\theta}\dot{\phi}\: sin\phi\)

• \(a_{\theta} = \frac{1}{R}\frac{d}{dt}(R^2\dot{\phi})+R\dot{\theta}^2\:sin\phi \: cos\phi\)

• \(a_{\theta} = \ddot{R} + R\dot{\phi}^2 + R\dot{\theta}^2cos^2\phi\)

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.