- #1
kiuhnm
- 66
- 1
When we solve Euler's differential equations for rigid bodies we find the angular acceleration ##\dot{\boldsymbol\omega}## and then the angular velocity ##\boldsymbol\omega##. Integrating ##\boldsymbol\omega## is less straightforward, so we start from a representation of the attitude, take its derivative and equate it to ##\boldsymbol\omega##.
The attitude can be represented as ##\boldsymbol\gamma=\phi\hat{\boldsymbol e}##, where ##\hat{\boldsymbol e}## is the principal axis of the rotation. In a course I'm watching online, the professor computes the derivative of ##\boldsymbol\gamma## as follows:$$
\dot{\boldsymbol\gamma} = \dot\phi \hat{\boldsymbol e}
$$
Wouldn't that be correct only for a fixed ##\hat{\boldsymbol e}##? Shouldn't we assume ##\hat{\boldsymbol e}## is changing in time as well?
The attitude can be represented as ##\boldsymbol\gamma=\phi\hat{\boldsymbol e}##, where ##\hat{\boldsymbol e}## is the principal axis of the rotation. In a course I'm watching online, the professor computes the derivative of ##\boldsymbol\gamma## as follows:$$
\dot{\boldsymbol\gamma} = \dot\phi \hat{\boldsymbol e}
$$
Wouldn't that be correct only for a fixed ##\hat{\boldsymbol e}##? Shouldn't we assume ##\hat{\boldsymbol e}## is changing in time as well?