0

I recently started to study flight dynamics and I have to derive the equations of motion of a plane from the Hamilton's Principle. To better understand this principle, it is needed to have some knowledge in Variational Principle and that's a little confusing for me, especially when applied to vectors.

For example, here someone also described the deduction of the equations of motion of a rigid body from Hamilton's Principle. It was defined the variation of the velocity vector as: $$ \delta\vec V = \delta \dot{\vec R_0} + \delta \vec \omega \times(\vec R_0 + \vec r) + \vec \omega \times \delta \vec R_0 + \delta \vec\theta \times \vec V $$

But I don't understand why the term $\delta \vec\theta \times \vec V$ appears. Could someone please help me with that?

Qmechanic
  • 220,844
WestC
  • 1

1 Answers1

1

Using the same description of the provided answer, and although you should be careful with freely exchanging $\delta \leftrightarrow \mathrm{d},$ one can see the last term coming from $\delta \vec{\theta} = \vec{\omega} \, \delta t.$

Nelson Vanegas A.
  • 835