# Particle moving in a rotating frame

1. Mar 29, 2010

### ian2012

There is an example in my lectures notes I am having trouble following through:

A particle moving in a rotating frame of angular velocity omega may be described by the Lagrangian:

$$L= \frac{1}{2} m ( \dot{\vec{r}} + \vec{\omega} \times \vec{r} )^{2}$$

N.B. $$\vec{r}.\vec{i} = x , \frac{d \vec{r} }{dx} = \vec{i}$$

Finding the equation of motion:

$$\frac{d}{dt} \frac{\partial L}{\partial \dot{q}} = \frac{\partial L}{\partial q}$$
$$\frac{\partial L}{\partial \dot{x}} = m [ \dot{x} + (\vec{\omega} \times \vec{r} ). \vec{i} ]$$

I don't understand how the last line came about?

It would mean that:

$$\frac{d \vec{r}}{dx} = \frac{d \dot{ \vec{r}}}{d \dot{x}} = \vec{i}$$

How do you prove the last part?

Last edited: Mar 30, 2010
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